Documented Elastomer-Mount Linear-Stiffness Worksheet
Calculate linear-model gravity deflection and undamped natural frequency from a documented or measured equivalent axial stiffness and the supported mass assigned to the same coordinate.
Controlled inputs
Use an equivalent stiffness for the actual mount assembly, axis, preload and boundary condition. A force/deflection pair yields only a secant stiffness for that pair.
Reference linear-model result
Equations and model boundary
For a positive equivalent translational stiffness K and effective supported mass M in a linear single-degree-of-freedom model:
The worksheet uses conventional standard gravity g0 = 9.80665 m/s² exactly only for the reference weight and gravity-deflection identity. Local gravity can be substituted outside this worksheet when required.
A force/deflection pair produces a secant stiffness between the two stated points. It is not automatically the tangent stiffness governing small perturbations and it is not automatically the dynamic storage stiffness governing a vibration test.
Exact unit normalization
Calculation is performed in N/m, kg and m. The exact bases are 1 in = 0.0254 m, 1 lbm = 0.45359237 kg and 1 lbf = 0.45359237×9.80665 N. Therefore 1 N/mm = 5.710147154733… lbf/in, not 0.00571015 lbf/in.
Reference check
| Girişlər | K | δlin | fn |
|---|---|---|---|
| K = 100 N/mm; M = 100 kg | 100000 N/m | 9.80665 mm | 5.03292121045 Hz |
| F = 1000 N; Δ = 10 mm; M = 100 kg | 100 N/mm | 9.80665 mm | same linear model |
What Shore A does and does not establish
ISO 48-4:2018, confirmed in 2024, specifies an indentation-hardness measurement method using Shore durometers. It does not publish a universal spring-stiffness equation for a finished mount in its public scope. ASTM D2240-15(2021) explicitly characterizes durometer hardness as an empirical control test and says no simple relationship exists between the measured indentation hardness and a fundamental material property.
A historical Gent correlation between Shore hardness and Young’s modulus is an approximate material correlation, not a complete mount model. Turning it into a mount stiffness additionally requires compound response, geometry, bonding/friction, compressibility and strain assumptions. This worksheet therefore does not implement that correlation.
Static versus dynamic elastomer behavior
ASTM D5992-96(2024) covers vibratory methods for measuring rubber stiffness, damping and dynamic modulus, including tests on full-scale products. A static catalog stiffness cannot silently be treated as dynamic storage stiffness. Record temperature, preload, frequency and amplitude with every stiffness value.
Source classification
| Claim | Təsnifat | Inspected source |
|---|---|---|
| Shore A is indentation hardness measured by a durometer | Current standard scope; no stiffness equation inferred | ISO 48-4:2018, edition 1, current and confirmed 2024 |
| Durometer hardness is empirical and has no simple relationship to a fundamental property | Current ASTM significance/use statement | ASTM D2240-15(2021), active; revision work item separately under development |
| Dynamic rubber stiffness/damping/modulus require vibratory measurement methods and conditions | Current ASTM guide scope | ASTM D5992-96(2024), active |
| δ = Mg/K and ωn = √(K/M) | General linear SDOF mechanics; not an ISO mount-selection formula | MIT OCW 2.003SC Engineering Dynamics, Recitation 10, rendered page 1 |
| inch, pound-mass and pound-force normalization | Metrology and exact definitions | NIST SP 811 Appendix B.8; BIPM 3rd CGPM Resolution 2 |
ISO 48-4:2018 official card — edition, status, confirmation and public scope.
ASTM D2240-15(2021) — active durometer-hardness method and public significance/use statement.
ASTM D5992-96(2024) — active dynamic-testing guide and public scope.
MIT OCW Recitation 10 notes — linear spring gravity deflection and undamped natural frequency.
NIST SP 811 Appendix B.8 and BIPM 3rd CGPM Resolution 2 — exact unit and conventional-gravity basis.
Accessed: 15 July 2026. The MIT PDF page was rendered and visually inspected. Only public ISO/ASTM scope/status text was used; no inaccessible clause, coefficient or limit was invented.
