Symbols

Unit

Designation

D_e

mm

Outside diameter

D_i

mm

Inside diameter

D_w

mm

Diameter at the root of slots in a disc spring

D_o

mm

Diameter of centre of rotation

E

N/mm²

Young’s modulus

F

N

Spring force of a single spring

F₁, F₂, F₃

N

Spring force for deflections s₁, s₂, s₃

F_c

N

Calculated spring force of a single spring when flat

F_ges

N

Spring force of a spring set or stack

ΔF

N

Force lost in setting

K₁, K₂, K₃, K₄

Constants for calculations

L_O

mm

Unloaded length of the spring stack or spring sets

L₁, L₂, L₃

mm

Length of the loaded spring stack or spring set for forces F₁, F₂, F₃

L_c

mm

Calculated length of the spring stack or set when springs are flat

N

Number of cycles to failure

R

N/mm

Spring rate

W

N/mm

Spring work

h_o

mm

Cone height of an unloaded single spring (calculated h_o = l_o – t)

h_o‘

mm

Cone height of an unloaded spring with reduced thickness t’ (and contact flats, calculated h_o=l_o– t)

i

No. of single springs or sets in series in a stack

l_o

mm

Height of an unloaded spring stack

n

No. of parallel springs in a set

s

mm

Deflection of a single spring

s₁, s₂, s₃

mm

Deflections relative to loads F₁, F₂, F₃

s_ges

mm

Deflection of a spring set or stack

t

mm

Thickness of individual

t’

mm

Reduced spring thickness for springs with contact flats (group 3)

W_M, w_R

Friction factors

δ= D_e/D_i

Diameter ratio

µ

Poisson’s ratio (for spring steel = 0.3)

σ

N/mm²

Calculated stress

σ_OM, σ_l, σ_ll, σ_lll, σ_lv

N/mm²

Calculated stress at points OM, I, II, III and IV as per figure 1

σ_o

N/mm²

Calculated maximum stress for springs with dynamic loads

σ_u

N/mm²

Calculated minimum stress for springs with dynamic loads

σ_h

N/mm²

Stress range for the working stroke of dynamically loaded springs

σ_O

N/mm²

Maximum stress for fatigue resistance

σ_U

N/mm²

Minimum stress for fatigue resistance

σ_H = σ₀ – σ_U

N/mm²

Permissible stress range for fatigue resistance