Analytical Solution of the General Linear Viscoelastic Radial Load Equation for Rotary Shaft Seals

Abstract

The viscoelastic radial load equation for a cylindrical shell representing the seal was derived from the static solution by the correspondence principle and from first principles. The equation decoupled in space and time by a normal mode analysis was solved both by conventional methods with an impact initial condition and rather more efficiently by the Laplace transform method, for a general linear Maxwell body in plane stress. The solution was in the form of a recurrence relation, allowing representation of material properties by any number of Maxwell elements. When subjected to the standard creep test, step radial load, the seal responded with an impact displacement, followed by transient and finally steady creep. The equation was also solved by the finite element method with the semidiscrete approximation. The solution for stress relaxation and oscillatory strain are given in the Appendix. Presented at the 47th Annual Meeting in Philadelphia, Pennsylvania May 4–7, 1992