Non-contact machining of spherical surface

Claim 1

A method of machining a spherical surface of a workpiece with a tubular jig which is rotatable about a first axis, a first end, a second end opposite to said first end, and a through passage extending along said axis from said first end to said second end, the passage having an inlet at the first end and an outlet at the second end, the outlet having a tapered surface spreading outwardly at a peripheral edge thereof, said method comprising the steps of: rotating the tubular jig about said first axis; rotating the workpiece about a second axis which is inclined a predetermined angle with respect to said first axis; supplying a fluid lubricant-coolant which contains suspended abrasive particles from said inlet through said passage toward said outlet, so that a highly packed flowing layer of abrasive particles is produced on and along said tapered surface under centrifugal forces generated by the rotation of said tubular jig; and pressing the spherical surface of the workpiece against said flowing layer of abrasive particles while said tubular jig and said workpiece are being rotated about said first and second axis, respectively, wherein said spherical surface of the workpiece has a radius of curvature R which is expressed by: ##EQU2## where θ is the angle of the tapered surface with respect to a plane which extends perpendicularly to said first axis, C is the outside diameter of the tapered surface, A is the distance from an outer edge of the tapered surface to the position where the workpiece is machined, and t is the thickness of the abrasive particle layer.

Claim 2

A method of machining a spherical surface of a workpiece with a tubular jig which is rotatable about a first axis, a first end, a second end opposite to said first end, and a through passage extending along said axis from said first end to said second end, the passage having an inlet at the first end and an outlet at the second end, the outlet having a tapered surface spreading outwardly at a peripheral edge thereof, said method comprising the steps of: rotating the tubular jig about said first axis; rotating the workpiece about a second axis which is inclined a predetermined angle with respect to said first axis; supplying a fluid lubricant-coolant which contains suspended abrasive particles from said inlet through said passage toward said outlet, so that a highly packed flowing layer of abrasive particles is produced on and along said tapered surface under centrifugal forces generated by the rotation of said tubular jig; and pressing the spherical surface of the workpiece against said flowing layer of abrasive particles while said tubular jig and said workpiece are being rotated about said first and second axis, respectively, wherein said spherical surface of the workpiece has a radius of curvature R which is expressed by: ##EQU2## where θ is the angle of the tapered surface with respect to a plane which extends perpendicularly to said first axis, C is the outside diameter of the tapered surface, A is the distance from an outer edge of the tapered surface to the position where the workpiece is machined, and t is the thickness of the abrasive particle layer.

Claim 7

A method of machining a spherical surface of a workpiece with a tubular jig which has a passage extending along a first axis thereof, said passage having a machining surface at a peripheral edge on an end thereof, said method comprising the steps of: rotating the tubular jig about said first axis; rotating the workpiece about a second axis which is inclined a predetermined angle with respect to said first axis; supplying a fluid lubricant-coolant which contains suspended abrasive particles into said passage so that a highly packed flowing layer of abrasive particles is produced on and along said machining surface under centrifugal forces generated by the rotation of said tubular jig; and pressing the spherical surface of the workpiece against said flowing layer of abrasive particles at one position of said machining surface to keep said end of said passage substantially entirely open while said tubular jig and said workpiece are being rotated about said first and second axes, respectively.

Claim 8

A method of machining a spherical surface of a workpiece with a tubular jig which has a passage extending along a first axis thereof, said passage having a machining surface at a peripheral edge on an end thereof, said method comprising the steps of: rotating the tubular jig about said first axis; rotating the workpiece about a second axis which is inclined a predetermined angle with respect to said first axis; supplying a fluid lubricant-coolant which contains suspended abrasive particles into said passage so that a highly packed flowing layer of abrasive particles is produced on and along said machining surface under centrifugal forces generated by the rotation of said tubular jig; and pressing the spherical surface of the workpiece against said flowing layer of abrasive particles at one position of said machining surface to keep said end of said passage substantially entirely open while said tubular jig and said workpiece are being rotated about said first and second axes, respectively.

Claim 11

A method of machining a spherical surface of a workpiece with a tubular jig which is rotatable about a first axis, a first end, a second end opposite to said first end, and a through passage extending along said axis from said first end to said second end, the passage having an inlet at the first end and an outlet at the second end, the outlet having a tapered surface spreading outwardly at a peripheral edge thereof, said method comprising the steps of: rotating the tubular jig about said first axis; rotating the workpiece about a second axis which is inclined a predetermined angle with respect to said first axis; supplying a fluid lubricant-coolant which contains suspended abrasive particles from said inlet through said passage toward said outlet, so that a highly packed flowing layer of abrasive particles is produced on and along said tapered surface under centrifugal forces generated by the rotation of said tubular jig; and pressing the spherical surface of the workpiece against said flowing layer of abrasive particles at one position of said tapered surface to keep said outlet substantially entirely open while said tubular jig and said workpiece are being rotated about said first and second axes, respectively.

Claim 12

A method of machining a spherical surface of a workpiece with a tubular jig which is rotatable about a first axis, a first end, a second end opposite to said first end, and a through passage extending along said axis from said first end to said second end, the passage having an inlet at the first end and an outlet at the second end, the outlet having a tapered surface spreading outwardly at a peripheral edge thereof, said method comprising the steps of: rotating the tubular jig about said first axis; rotating the workpiece about a second axis which is inclined a predetermined angle with respect to said first axis; supplying a fluid lubricant-coolant which contains suspended abrasive particles from said inlet through said passage toward said outlet, so that a highly packed flowing layer of abrasive particles is produced on and along said tapered surface under centrifugal forces generated by the rotation of said tubular jig; and pressing the spherical surface of the workpiece against said flowing layer of abrasive particles at one position of said tapered surface to keep said outlet substantially entirely open while said tubular jig and said workpiece are being rotated about said first and second axes, respectively.