Basic Belleville Spring Calculation
The calculation is carried out in metric or English units. With the ANSI standard set, the calculation is performed in English units.
The calculation is done in XY and XZ planes and their quadratic sum is made.
Calculated Parameters
Unloaded height of truncated cone of free spring
h = H - t [mm, in]
where:
H | unloaded spring height [mm, in] | |
t | spring material thickness [mm, in] |
Diameter ratio
where:
D | outer spring diameter [mm, in] | |
d | inner spring diameter [mm, in] |
Calculation factor α
Calculation factor β
Calculation factor γ
Limit washer deflection
s m = h [mm, in]
where:
h | unloaded height of truncated cone of free spring [mm, in] |
Force at maximum spring deflection (at limit deflection)
where:
E | spring modulus of elasticity [MPa, psi] | |
t | spring material thickness [mm, in] | |
s m | limit spring deflection [mm, in] | |
| μ | Poisson's ratio [-] | |
| α | calculation factor [-] | |
D | outside spring diameter [mm, in] |
Force exerted by the spring at the s deflection
where:
Maximum pressure stress in the spring at the s deflection
where:
Total spring number in a set
χ = n i [-]
where:
n | spring number in a set with unidirectional mounting [-] | |
i | spring number in a set with opposite mounting or number of sets with unidirectional mounting in a set with combined mounting [-] |
Stroke (deflection) of a spring set
z = i s [mm, in]
where:
i | spring number in a set with opposite mounting or number of sets with unidirectional mounting in a set with combined mounting [-] | |
s | working deflection of a spring [mm, in] |
Force exerted by a spring set
F = n F 1 [N, lb]
where:
n | spring number in a set with unidirectional mounting [-] | |
F 1 | force exerted by one washer [N, lb] |
Length of spring set in unloaded state
L 0 = i (h + n t ) [mm, in]
where:
Length of loaded spring set
L = L 0 - z [mm, in]
where:
L 0 | length of spring set in unloaded state [mm, in] | |
z | stroke (deflection) of spring set [mm, in] |
Review of all used variables: