## Spring Design

which are the basis of spring design, can be found here.

### The Spring Index

The spring index (c) is the relationship between the coil mean diameter D and wire diameter d (c=D/d). When designing a rectangular wire helical spring, it is preferable to set the spring index within the range of 4 to 15. Be careful as a decrease in the spring index leads to an increase in the local stress.

# In this part, we will use an answer to a question that was sent to us before to explain this.

Q. Do compression coil springs with the same cross-sectional area but different cross-sectional shapes (round and square) have the same spring constant? Also please provide me the spring constant’s calculation formula, if it is okay for you.
A. For example, if the material’s cross-section area of both springs is 25mm2:

①　Compression spring:
– Wire diameter: Ø5.64
– Coil mean diameter: 30mm
– Free length: 40mm
– Number of active coils: 3
– Total number of coils: 5
– Spring constant’s calculation formula:
k=(G x d＾4)/(8 x Na x D＾3)
Spring constant: k=1210.1N/mm

②　Rectangular wire helical spring
– Material dimensions: (5×5)
– Coil mean diameter: 30mm
– Free length: 40mm
– Number of active coils: 3
– Total number of coils: 5
– Spring constant’s calculation formula:
k=(G x t＾4)/(5.6 x Na x D＾3)
Spring constant: k=1060.1N/mm

*When using the spring constant’s calculation formula for rectangular wire helical springs, a separate coefficient for each shape is required.
From the results above and as shown on Fig.1, the spring constants get lower according to the following order: round > square > rectangle cross-section.

Fig.1. Relation between materials’ cross-section shapes and spring constants (in case of the same area)