A self-centering grinding wheel assembly that includes a spindle shaft including a conical-shaped end, a grinding wheel, and a grinding wheel adapter. The grinding wheel adapter affixed to the grinding wheel. A plurality of alignment members disposed radially within the grinding wheel adapter. Each of the plurality of alignment members include a tapered surface that conforms to a conical end of the spindle shaft. The plurality of alignment members slide radially with the grinding wheel adapter. The plurality of alignment members self-center the grinding wheel adapter on the spindle shaft in response to the grinding wheel adapter being assembled to the conical end of the conical shaft.