Page 710 - Mechanical Engineers' Handbook (Volume 2)

3 Numerical Controllers 701

rate at which the uncut surface of the workpiece passes the cutting edge of the tool, usually
expressed in millimeters per minute or inches per minutes. The rate of metal removal is
given by the product of the cutting speed, the feed rate, and the depth of cut. The cutting
speed and the feed rate are the two most important parameters that a machine operator can
adjust to achieve optimum cutting conditions.

3.3 Point-to-Point and Contouring Numerical Controllers
In the example of the preceding section, the drill must be moved to the center of the hole
before the drilling operation starts. The drill can start from the origin and traverse to the
center of the hole. The machine tool may first move along the x axis by 1.5 in., followed
by a movement along the y axis by 2.5 in. It may also simultaneously start moving along
the x and y axes. A numerical controller that can position the tool at specified locations
without control over the path of the tool between locations is called a point-to-point or
positioning controller. 13 A positioning controller may be able to move along a straight line
at 45 by simultaneously driving its axes.
A contouring controller provides control over the tool path between positions. For in-
stance, the tool can trace the boundary of a complex part with linear and circular segments
in one continuous motion without stopping. For this reason, contouring controllers are also
called continuous-path machines. The controller can direct the tool along straight lines,
circular arcs, and several other geometric curves. The user specifies a desired contour which
is typically the boundary or shape of a complex part, and the controller performs the appro-
priate calculations to continuously drive two or more axes at varying rates to follow this
contour.
The specification of a contour in point-to-point NC is tedious because it takes a large
number of short connected lines to generate a contour such as a circular arc. The programmer
must also provide the appropriate feed rates along these short straight-line segments to con-
trol the speed along the contour.

NC Interpolators
In multiaxis contoured NC, multiple independently driven axes are moved in a coordinated
manner to direct the tool along a desired path. An interpolator generates the signals to drive
the servoloops of multiple actuators along a desired tool path. 21 The interpolator generates
a large number of intermediate points along the tool path. The spacing between the inter-
mediate points determines the tool accuracy in tracking the desired path. The closer the
points are, the better the accuracy. At each interpolated point along the tool path, the positions
of the multiple axes are computed by a kinematic transformation. By successively com-
manding the NC axes to move from one intermediate point to the next, the tool traces a
desired contour with respect to the part.
Older NC systems contained hardware interpolators such as integrators, exponential
deceleration circuits, linear interpolators, and circular interpolators. Most of today’s numer-
ical controllers use a software interpolator. The software interpolator takes as input the
type of curve (linear, circular, parabola, spline, etc.), the start and end points, parameters
of the curve such as the radius and the center of a circle, and the speed and acceleration
along the curve. The interpolator feeds the input data into a computer program that generates
the intermediate target points along the desired curve. At each intermediate target point, the
interpolator generates the commands to drive the servoloops of the actuators. The servoloops
are closed outside of the interpolator. Several excellent references provide details on closed-
loop control of servoactuators. 22,23