Method of machining a workpiece in a turret lathe and an nc lathe for performing this method

In an NC lathe, comprising a main spindle mounted for rotation in a spindle stock about a main spindle axis;

• a main motor for rotatably driving said main spindle about said main spindle axis;
• a workpiece chuck means mounted on said main spindle;
• a tool turret arranged adjacent said main spindle;
• means for rotatably mounting said tool turret;
• means for rotatably driving said tool turret about a tool turret axis parallel to the main spindle axis;
• said tool turret comprising a turret body and at least one turret spindle for holding a tool rotatably mounted in said turret body;
• means for rotatably driving said turret spindle about a turret spindle axis extending radially to the turret axis;
• a carriage bearing said tool turret for slidable displacement transversely to the main spindle axis, and a carriage drive for slidably displacing said carriage, the improvement comprising NC control means operatively connected to said main motor, the tool turret driving means, and said carriage drive for effecting controlled, stepless, transverse displacement of the carriage and controlled stepless rotation of the main spindle and of the tool turret such that simultaneously
• (a) the main spindle is rotated about the main spindle axis in a defined direction of rotation and with a defined angular velocity d.gamma./dt;
• (b) the turret spindle is rotated about the turret spindle axis;
• (c) the turret is rotated about the turret axis in the defined direction of rotation and with said defined angular velocity;
• (d) the carriage is displaced transversely to the main spindle axis at a velocity dX/dt
• said velocities being the first derivatives of the following equations:
• ##EQU4## wherein t, .gamma., X, A, Y.sub.o, and v.sub.y denote the following:
• t=the time which is equal to zero when a tool carried by said turret spindle touches a workpiece carried by said chuck means for the first time;
• .gamma.=the angle between the turret spindle axis and a first plane defined by the main spindle axis and the turret axis;
• X=the distance of the turret axis from the main spindle axis;
• A=the distance of the turret axis from the normal projection of the main spindle axis onto a second plane defined by the turret axis and the turret spindle axis, which plane pivots about the turret axis;
• Y=the distance of the main spindle axis from said second plane, with Y.sub.o being the value of Y when t equals zero;
• v.sub.y =the feed velocity dy/dt of the turret spindle axis relative to the main spindle axis in the direction of diminishing values of Y.