Analysis and Design of Machine Elements

14 Springs

Nomenclature

b

slenderness ratio

C

spring index

D

mean diameter, mm

D _i

inside diameter, mm

D _o

outside diameter, mm

d

spring wire diameter, mm

E

modulus of elasticity, MPa

F

external axial force, N

f _n

fundamental natural frequency, Hz

G

shear modulus, MPa

g

gravity acceleration, m s⁻²

H _f

free height/length of spring, mm

H _h

length of hook, mm

H _i

installed height/length, mm

H _o

operating height/length, mm

H _s

solid height/length, mm

h

working distance of a spring, mm

I

moment of inertia of spring wire, mm⁴

J

polar moment of inertia, mm⁴

K _w

Wahl factor

K _wT

Wahl factor for torsion spring

k

spring rate, N mm⁻¹, N m⁻¹

k _ϕ

spring rate of torsion spring, N mm/(°)

L

length of wire, mm

M

bending moment, N mm

m

mass of spring, kg

n

number of active coils

n _total

total number of coils

p

spring pitch, mm

S

shear force, N

S _ca

fatigue strength safety factor

T

torsional moment, N mm

U

strain energy, J

U ₀

energy loss due to friction, J

W

section modulus, mm³

w

work for a deflection under a load, J

α

pitch angle, °

δ

coil clearance, mm

δ ₁

coil clearance at the maximum load, mm

λ

deflection, mm

ρ

density, kg m⁻³

σ

bending stress, MPa

σ _b

ultimate tensile ...