A tool for use in an abrasive machining process has a body extending along a central longitudinal axis from a first end to a tip end. An abrasive material is located on the tip end. The body has a tip end protuberance. An abrasive material is located on the protuberance. A body lateral surface has, over a radial span of at least 20% of a radius of the protuberance, a continuously concave longitudinal profile diverging tipward.