Patent ID: 8911153

Claim:
An elastomeric spherical bearing comprising: a multitude of elastomeric layers defined about a bearing focal point; and a multitude of shims, each of said multitude of shims mounted between at least two of said multiple of elastomeric layers, a first shim of said multitude of shims having a first thickness and a second shim of said multitude of shims having a second thickness, said second thickness different than said first thickness such that said first and second shims are subject to substantially the same stress to satisfy: σ θ = 4 · ( B I - ( B o - β ) ) · ( γ a + γ r ) · G · D · π · E · cos ⁡ ( B s ) · R s 1800 · T e · R s · sin ⁡ ( B s ) · N s · T ( T T N s + 1 ) · T T N s · T ^ s + T T · [ [ E · T s ⁡ [ cos ⁡ ( B s ) ] 2 4 · E · T s 3 12 · ( 1 - μ 2 ) · [ R s · sin ⁡ ( B s ) ] 2 ] 1 / 4 ] - 3 where: {circumflex over (T)} e =Average Elastomer Thickness ( T i + T i + 1 ) 2 (in) T s =Shim Thickness T s j (in) T{circumflex over (T)} s =Average Shim Thickness (in) μ=Shim Poison Ratio E=Shim Modulus of Elasticity (psi) R s =Shim Median Spherical Radius R j (in) G=Average Elastomer Shear Modulus ( G i + G i + 1 ) 2 (psi) B I =Bearing Inner Wrap Angle (deg) B o =Bearing Outer Wrap Angle (deg) N s =Total Number of Shims B s =Outer Wrap Around Angle of Shim B s j (deg) D=Shim Bending Stiffness Term (lb-in) B ET =Shim Geometric Stiffness Term (in) γ=Average Elastomer Compression Induced Shear Strain (in/in)/100 T T =Total Bearing Elastomer Thickness (in) Q=Averaging Coefficient of Bearing (non-dimensional) υ=Averaging Coefficient of Elastomer To Shim Context (non-dimensional) L L =Unsupported Spherical Arc of Shim L L i (see FIG. 4 ) Y Y =Radial Deflection of Shim Y Y i (see FIG. 4 ) σ θ =Shim Hoop Stress σ θi (psi) D P =Differential Resultant Pressure Load On Unsupported Spherical Arc of Shim L L i T c =Axial Compressive Load (lb) θ=Torsional Motion Angle (deg) β=Cocking Motion Angle (deg) T c ·sin·β=Radial Load (lb) R I =Bearing Inner Radius (in) R o =Bearing Outer Radius (in) T e i =Elastomer Thickness (in) α=Bearing Outer Taper Angle (deg).