164 Volute springs have been used in some terrestrial applications such as vertical and horizontal suspension  systems for tanks  and smaller tools like  garden shears  where a compact or self -guided spring is required.  Since there are not a wide variety of applications that require the unique characteristics of a volute spring  and the relatively high manuf acturing cost, there are  not as many off -the-shelf configurations that are  considered vendor standard parts when compared to wire compression springs . This means that a detailed  analysis and custom design is likely required for each application which contr ibute to the higher unit price  of volute springs.   

Figure 2.  Terrestrial uses for volute springs   In general, aerospace applications have much more stringent requirements that  require substantial ly more  design margin than terrestrial applications . Custom design parts are frequently employed to meet these  requirements as slightly more expensive mechanical piece parts can substantially  reduce the system -level  cost. One of the most critical requirements, for satellites i n particular, is that the overall envelope of the  spacecraft fits inside the launch vehicle fairings. The deployables and the LRAs that restrain them are  generally at the very perimeter  of this  overall envelope which makes a compact design a requirement . The  volute spring was ideal for this  application for that reason.  

Design and Analysis  

Aerospace parts are upheld to a significantly higher standard than their  terrestrial counterparts. Space  environments such as extreme temperatures, vacuum, launch loadi ng and payload restrictions often dictate  special materials, processes and coatings. Furthermore, mechanical parts often require rigorous analysis  to determine both output force margin and internal stress margins to ensure the adequacy of the design. As su ch, a solid unders tanding of the spring functions and analysis was required to justify its usage.   During compression, a volute spring essentially takes the applied axial load and bends the centerline of the spring bar downwards. The deflection begins at t he largest coil of the spring which has the lowest spring  constant. As the spring is compressed, the load is spread through subsequent coils  until the point where  the largest coil bottoms out, known as the i nitial bottoming l oad. After initial bottoming occurs , the load vs  deflection curve changes from linear to  exponential . This happens because spring force in each subsequent  coil increases as the diameter of the coil decreases . This results in a curve that asymptotes  at a peak high  force at the solid he ight as shown in Figure 5. The point at which the smallest spring coil bottoms out is  called the Final Bottoming Load. The peak of the Load vs Deflecti on curve is determined by the spring  constant of the final coil  because it is the stiffest coil in a standard volute spring.    Figure 3 illustrates the key parameters and variables  required to perform  the volute spring design analysis .  The image on the right illustrates an unwound volute spring with ground ends.  Based on the spring geometry  parameters, the spring load, deflection, and stress can be calculated using the equations in Figure 4. The  spring load is used to determine the force that the spring is capable of providing. The spring deflection  equations are used to calculate how much the spring compresses axially under a known load. Lastly, the  shear stress determines the internal stress in the coils when under an axial load.