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They are used in the same applications as fender washers. A spherical washer is part of a self-aligning nut; it is a washer with one radiused surface, which is designed to be used in conjunction with a mating nut in order to correct for up to several degrees of misalignment between parts.
A plain washer (or 'flat washer') is a flat annulus or ring, often of metal, used to spread the load of a screwed fastening. Additionally, a plain washer may be used when the hole is a larger diameter than the fixing nut.