Single-sided four-way indexable positive cutting insert and insert mill therefor

A single-sided, four-way indexable cutting insert having a positive basic shape and comprising:

• a rake surface;
• a base bearing surface located opposite the rake surface;
• an insert axis AI extending perpendicular to the base bearing surface and through a center of the insert, the insert axis defining:
• an upward direction from the base bearing surface towards the rake surface, a downward direction opposite to the upward direction, and an outward direction perpendicular to the upward and downward directions and extending away from the insert axis;
• a cutting insert height HI measurable parallel to the insert axis, from the base bearing surface to a highest point of the rake surface;
• a peripheral surface connecting the rake surface and base bearing surface, the peripheral surface comprising:
• an unground lower sub-surface which extends upwardly and outwardly from the base bearing surface, the lower sub-surface comprising first, second, third and fourth side abutment surfaces;
• and
• an upper sub-surface connecting the lower sub-surface and the rake surface, the upper sub-surface beginning in the upward direction at a minimum upper surface height HU above the base bearing surface;
• a cutting edge formed along an intersection of the peripheral surface and rake surface;
• and
• a screw hole opening out to the rake and base bearing surfaces, the screw hole having a void volume VS;
• wherein:
• the insert has an imaginary square frustum defined by:
• a square base containing the base bearing surface;
• four isosceles trapezoid side surfaces, each extending upwardly and outwardly from the square base at an abutment surface relief angle θ fulfilling the condition 1°≤θ≤15°, and each containing a respective one of the first, second, third and fourth side abutment surfaces;
• and
• a square top connecting the four isosceles trapezoid side surfaces and located a distance equal to the cutting insert height HI from the square base;
• the upper sub-surface comprises at least one overhanging portion, which extends outwardly from an adjacent one of the trapezoid side surfaces and has a lowermost point at said minimum upper sub-surface height HU;
• in a view parallel to the insert axis AI, an inscribed circle diameter IC of the cutting edges fulfills the condition IC≤10 mm;
• a volume ratio VS/VF of the void volume VS and a material volume VF of the cutting insert fulfills the condition VS/VF≥0.25;
• and
• the peripheral surface further comprises a first side non-abutment surface adjacent to the first side abutment surface, a second side non-abutment surface adjacent to the second side abutment surface, a third side non-abutment surface adjacent to the third side abutment surface and a fourth side non-abutment surface adjacent to the fourth side abutment surface;
• wherein each of the first, second, third and fourth non-abutment surfaces are spaced further from the central axis than the first, second, third and fourth abutment surfaces.