231
OF ENGINEERING FORM ULÆ.
Helical and Volute Swung«.
helical.
VOLUTE.
E = Modulus of elasticity in tons.
R = Menu radius of spring in inches.
I = Moment of inertia of section of spring.
D = Diameter of spring steel if round in inches.
b = Breadth of rectangular or square section in Inches.
d — Depth of rectangular section in inches.
E = Deflection of spring in inches.
T = Modulus of torsion about | E.
= Number of revolutions of spring.
W = Working load, tons.
3 4’72
W = -g- for round steel; = —— for square steel.
6 • 67 <72
W = --------— — - for rectangular steel.
K bi + d'i
Ra W 2 it n 64 n W R3
F sz---pr------- = —;p~j—— for round steel;
R3 w 12 ti- n . Rs w (&2 + <Z2) 6 7T n
=--------------- for square; = ------w,- .. ,,—■— •
T jrt h » 1’. a d
These formulæ refer to helical springs, but they may be
made to apply approximately to volute springs. The deflec-
tion of volute springs is, however, not directly proportional
to the load, but increases somewhat slowly with heavy pres-
sure. The section of a volute spring should gradually
diminish from the base to the apex. The offsets of the volute
spring should vary as the cube of the radius It. In conical
springs, with constant cross sections of steel, the deflection
equals from i to | that of a cylindrical spring whose radius
equals that of the base of the cone.