Vortex pinning affects neutron-star free precession by modifying its frequency and geometry, in a gyroscopic effect. For neutron stars with low oblateness, the free-precession frequency is given by the product of the ratio of moments of inertia of the pinned superfluid to the rigid component of the rest of the star times half the superfluid vorticity. This poses a severe difficulty for any interpretation of the 35-day cycle of Her X-1 in terms of neutron-star wobble if vortex pinning exists.
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J. Shaham (1977) studied this question.