Finite Element Solution of the Radial Load Equation for Rotary Shaft Seals

Abstract

Displacement equations for static conical seal structures were solved by the Ritz-Galerkin finite element method. The constitutive equation was Hooke's law with the plane stress assumption. Finite strains relative to the initial or free configuration were used in conjunction with the strain-dependent modulus of the material. The nonlinearity of the transverse shear stress resultant or radial load thus predicted, was in exact agreement with the experiment almost up to the maximum possible displacement. The mechanism by which the radial load became nonlinear was not simply additive in the geometric and material contributions. Instead, the geometric non-linearity, while having a negligible effect by itself on the radial load, had the property of more than doubling the maximum strain in the structure, therefore amplifying the effect of the strain-dependent modulus on the radial load. Both local and global algorithms for solving nonlinear equations gave the same results, suggesting that the solution found was unique. Experimental radial loads of seal structures with radius-to-thickness ratios between 6 and 42 were favorably predicted by the program. Measured seal thermal expansions were also in very good agreement with program predictions.