A multiple disc grinding machine comprising - a driving shaft, - a plurality of abrasive discs combined in a pack on said shaft, each of said discs comprising a disc-shaped support having a circumferential rim on which abrasive cutting sectors are applied and an opposing central hole for fitting on to the driving shaft of the grinding machine, said hole extending through the thickness of the disc-shaped support, and the hole has a first cylindrical through section which comes into coupling contact with the driving shaft, - at least one radial recess is formed on a front surface of the disc-shaped support, - the driving shaft is provided with an internal axial duct for supplying the coolant fluid, said duct being continued by at least one radial end hole opening at the location of the cylindrical shell of the end portion of the shaft designed to house the abrasive discs, the thickness of the disc in contact with the shaft and the radial end hole being smaller than the diameter of the radial end hole provided on the shaft; the machine being characterised in that - a portion of said central hole has a diameter greater than the diameter of the connection to said shaft, such that an annular chamber is formed in the thickness of the support, and wherein - the central hole has a second cylindrical through section extending as an axial continuation of the first section, said second section having the diameter greater than the first section, such that said annular chamber is formed at the location of the second through section, following connection with the shaft, - the at least one radial recess is extending from said annular chamber towards the circumferential rim of said disc, in such a way that a coolant fluid fed into the driving shaft can accumulate in said annular chamber and can then flow through said radial recess towards the abrasive edge of said disc, and wherein - the front surface of each of said abrasive discs in said pack abuts against a corresponding surface of the adjacent abrasive disc, and wherein axial clamping action of the pack of the abrasive discs causes said surfaces to act as friction members which prevent relative sliding of adjacent ones of the abrasive discs, and wherein a passage for the coolant fluid from the chamber containing the fluid to the recesses is ensured, said recesses therefore forming a kind of channel for supplying the fluid to the exterior of the disc in order to distribute the fluid to the processing zones close to the abrasive sectors of the circumferential rim. - a driving shaft, - a plurality of abrasive discs combined in a pack on said shaft, each of said discs comprising a disc-shaped support having a circumferential rim on which abrasive cutting sectors are applied and an opposing central hole for fitting on to the driving shaft of the grinding machine, said hole extending through the thickness of the disc-shaped support, and the hole has a first cylindrical through section which comes into coupling contact with the driving shaft, - at least one radial recess is formed on a front surface of the disc-shaped support, - the driving shaft is provided with an internal axial duct for supplying the coolant fluid, said duct being continued by at least one radial end hole opening at the location of the cylindrical shell of the end portion of the shaft designed to house the abrasive discs, the thickness of the disc in contact with the shaft and the radial end hole being smaller than the diameter of the radial end hole provided on the shaft; - a portion of said central hole has a diameter greater than the diameter of the connection to said shaft, such that an annular chamber is formed in the thickness of the support, and wherein - the central hole has a second cylindrical through section extending as an axial continuation of the first section, said second section having the diameter greater than the first section, such that said annular chamber is formed at the location of the second through section, following connection with the shaft, - the at least one radial recess is extending from said annular chamber towards the circumferential rim of said disc, in such a way that a coolant fluid fed into the driving shaft can accumulate in said annular chamber and can then flow through said radial recess towards the abrasive edge of said disc, and wherein - the front surface of each of said abrasive discs in said pack abuts against a corresponding surface of the adjacent abrasive disc, and wherein axial clamping action of the pack of the abrasive discs causes said surfaces to act as friction members which prevent relative sliding of adjacent ones of the abrasive discs, and wherein