Machining method employing oblique workpiece spindle

A machining method used to machine a predetermined curved surface on a workpiece comprising:

• (1) providing a machining apparatus, the machining apparatus comprising at least one vertical tool spindle for mounting a tool and a workpiece spindle being rotatable in an axis thereof, the at least one tool spindle being rotatable relative to a vertical direction, wherein a rotational axis of the workpiece spindle is oblique relative to a rotational axis of the at least one tool spindle, an angle defined by the axis of the workpiece spindle relative to the rotational axis of the tool spindle is 45 degrees, the machining apparatus further comprising at least one first rail parallel to one of the vertical direction, at least one second rail perpendicular to the first rail, at least one third rail perpendicular to the first rail and the second rail, a base, a horizontal slider, a vertical slider, a lateral crossbeam, and a lateral slider, the tool spindle being slidable in directions of the at least one first rail, the second rail, and the third rail, the base comprising two support beams and the second rail, the two support beams separately formed on a top surface of the base and extending parallely along the vertical direction, the horizontal slider slidably attached on the second rail, the first rail defined in the horizontal slider, the vertical slider engaged in the first rail, the lateral crossbeam extending from the vertical slider, the third rail defined in the lateral crossbeam, the lateral slider engaged with the third rail;
• (2) mounting the workpiece onto the workpiece spindle;
• (3) driving the spindle and the workpiece spindle to rotate, and positioning the tool corresponding to the workpiece;
• and (4) driving a machining point of the tool to move on the predetermined curved surface and along a path passing through a top point and any point of an edge of the predetermined curved surface.