Determining the length of a material in a volute spring

[DominicG]

Does anyone know of a formula to determine the length of material in a volute spring?

The given data would be:
ID
OD
Material thickness
Material Width
Clearance between coils

Thanks,
Dominic

 

[renderu]

I think you can use the equations for a Archimedean spiral:

http://www.intmath.com/blog/length-of-an-archimedian-spiral/6595

 

[zekeman]

t=thickness
c=clearance
R0=OD
Ri=ID
dr/d@=(t+c)/6.28=x;d@/dr=1/x
ds =SQRT(r^2+(dr/d@)^2)=approx rd@
integral rd@ limits Ri to R0-t
rd@=(rd@/dr)dr =1/x(rdr)
integrating
1/x(r^2/2) limits Ri to R0-t
L=1/2x{(R0-t)^2-Ri^2}