Formulas to obtain mechanical properties of elastomeric bearing

PropertyNotationFormula
Single rubber layer thickness${{t}_{r}}$
Number of rubber layers$n$
Steel shim thickness${{t}_{s}}$
Outer diameter${{D}_{o}}$
Inner/lead core diameter${{D}_{i}}$
Rubber cover thickness${{t}_{c}}$
Shear modulus$G$
Bulk modulus of rubber${{K}_{bulk}}$
Yield stress of lead${{\sigma }_{L}}$
Density of bearing${{\rho }_{b}}$
Total rubber layer thickness$t_r$ $n{{t}_{r}}$
Total height$h$$n{{t}_{r}}+(n-1){{t}_{s}}$
Bonded rubber area$A$$\frac{\pi }{4}\left[ {{\left( {{D}_{o}}+{{t}_{c}} \right)}^{2}}-D_{i}^{2} \right]$
Lead area${{A}_{L}}$$\frac{\pi }{4}D_{i}^{2}$
Characteristic strength${{Q}_{d}}$${{\sigma }_{L}}{{A}_{L}}$
Yield displacement$Y$
Shape factor$S$$\frac{{{D}_{o}}-{{D}_{i}}}{4{{t}_{r}}}$
Moment of inertia$I$$\frac{\pi }{64}\left[ {{\left( {{D}_{o}}+{{t}_{c}} \right)}^{4}}-D_{i}^{4} \right]$
Adjusted moment of inertia${{I}_{s}}$$I\frac{h}{{{T}_{r}}}$
Volume of bearing${{V}_{b}}$$Ah$
Mass of bearing${{m}_{b}}$${{\rho }_{b}}{{V}_{b}}$
Diameter ratio${{r}_{d}}$$\frac{{{D}_{o}}}{{{D}_{i}}}$
Central hole factor$F$$\frac{{{\left( {{r}_{d}} \right)}^{2}}+1}{{{\left( {{r}_{d}}-1 \right)}^{2}}}+\frac{1+{{r}_{d}}}{\left( 1-{{r}_{d}} \right)\ln \left( {{r}_{d}} \right)}$
Compression modulus${{E}_{c}}$${{\left( \frac{1}{6G{{S}^{2}}F}+\frac{4}{3{{K}_{bulk}}} \right)}^{-1}}$
Rotational modulus${{E}_{r}}$$\frac{{{E}_{c}}}{3}$
Vertical stiffness${{K}_{v}}$$\frac{A{{E}_{c}}}{{{T}_{r}}}$
Horizontal post yield stiffness${{K}_{d}}$$\frac{GA}{{{T}_{r}}}$
Horizontal yield strength${{F}_{Y}}$${{Q}_{d}}+{{K}_{d}}Y$
Horizontal elastic stiffness${{K}_{el}}$ (${{K}_{1}}$)$\frac{{{F}_{Y}}}{Y}$
Stiffness ratio$\alpha $$\frac{{{K}_{d}}}{{{K}_{el}}}$ $\left( =\frac{{{K}_{2}}}{{{K}_{1}}} \right)$
Torsional stiffness${{K}_{t}}$$\frac{2G{{I}_{s}}}{h}$
Rotational stiffness${{K}_{r}}$$\frac{{{E}_{r}}{{I}_{s}}}{h}$
Critical buckling load${{P}_{cr}}$$\frac{\pi \sqrt{{{E}_{r}}GI{{A}_{0}}}}{{{T}_{r}}}$
Critical buckling displacement${{u}_{cr}}$$\frac{{{P}_{cr}}}{{{K}_{v0}}}$
Cavitation force${{F}_{c}}$$3G{{A}_{0}}$
Cavitation displacement${{u}_{c}}$$\frac{{{F}_{c}}}{{{K}_{v0}}}$


The excel sheet web application to calculate these properties are available here:
Bearing Properties Calculation