What is One Dimensional and Two Dimensional Lathe Turning Operations

One Dimensional Lathe turning Operations: 

In one-dimensional turning, a (single-point) cutting tool mounted on a carriage travels parallel to the axis of rotation of the workpiece, normally held by a chuck and a tailstock (for longer parts)  This feed motion of the tool reduces the radius of the rotational workpiece by an amount equal to the depth of the cut in a direction normal to the feed motion axis (in the same plane).

Two Dimensional Lathe turning Operations: 

In two-dimensional turning, the tool travels and cuts into the workpiece in the feed direction as well as in the perpendicular depth of- cut direction, thus yielding workpiece profiles with a variable diameter (Fig. 1).

Both one-dimensional and two-dimensional turning operations can be carried out on manual or on automatically controlled lathes

The major process variables in turning are the feed rate, f, the cutting velocity, V, and the depth of cut, a. The feed rate of turning is equal to the travel rate of the tool in the feed direction, normally defined in the units of mm/rev (or inches/rev)—i.e., distance traveled by the tool per each revolution
of the spindle/workpiece.

The cutting velocity of turning refers to the linear velocity of the workpiece at the point of contact with the tool:

V= 3.14N [ (d1+d2 ) /2 ]

where,
N is the spindle’s (i.e., workpiece’s) rotational speed, defined in the units of revolutions per minute (rpm), 
d1 and d2 refer to the initial and postcutting diameters of the workpiece, respectively, defined in the units of meters or feet, together, yielding the units of m/min (or ft/min) for V

Turning of a workpiece is normally carried in several passes: in the first pass (or several initial passes), the objective is removal of material at increased rates (achieved by selecting a high feed rate) at the expense of surface finish quality; and in the last fine-turning pass the objective is meeting dimensional integrity and surface quality requirements using a reduced feed rate for the same cutting velocity, so that for each rotation of the spindle, the distance that the tool travels in the feed direction is considerably shortened, thus providing maximum continuity on the workpiece’s surface.