Milling Calculations 295
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Class Outline
Class Outline
Objectives
The Purpose of Toolpath Calculations
Program Zero Location
Face Milling Calculations
The Face Milling Toolpath: Y-Axis
The Face Milling Toolpath: X-Axis
Pocket Milling Calculations
The Pocket Toolpath
Spot Drilling Calculations
The Spot Drill Toolpath
Drilling Calculations
The Drilling Toolpath
CRC on the Mill
Full-Circle Milling Calculations
The Full Circle Toolpath
The Bolt Hole Pattern
Summary
Lesson: 1/17
Objectives
l Describe the basic elements of a toolpath.
l Identify the appropriate location for program zero on a part.
l Explain the general rules that govern face milling calculations.
l Calculate the Y-axis locations for a common face milling operation.
l Calculate the X-axis locations for a common face milling operation.
l Explain the general rules that govern pocket milling calculations.
l Calculate the initial coordinates to begin a boxing routine for a rectangular pocket.
l Explain the general rules that govern spot drilling calculations.
l Calculate the depth required to leave a chamfer with a spot drill.
l Explain the general rules that govern drilling calculations.
l Calculate the depth required to completely drill a hole.
l Explain a common method for removing ramping motions from a program’s toolpaths.
l Explain the general rules that govern full-circle milling.
l Calculate the starting locations for matching full radius and arc in motions.
l Calculate the coordinate location of a hole in a bolt-hole pattern.
Figure 1. Face milling operations require
calculations to find the X- and Y-axis positions
for each facing pass.
Copyright © 2015 Tooling U, LLC. All Rights Reserved.
Lesson: 1/17
Objectives
l Describe the basic elements of a toolpath.
l Identify the appropriate location for program zero on a part.
l Explain the general rules that govern face milling calculations.
l Calculate the Y-axis locations for a common face milling operation.
l Calculate the X-axis locations for a common face milling operation.
l Explain the general rules that govern pocket milling calculations.
l Calculate the initial coordinates to begin a boxing routine for a rectangular pocket.
l Explain the general rules that govern spot drilling calculations.
l Calculate the depth required to leave a chamfer with a spot drill.
l Explain the general rules that govern drilling calculations.
l Calculate the depth required to completely drill a hole.
l Explain a common method for removing ramping motions from a program’s toolpaths.
l Explain the general rules that govern full-circle milling.
l Calculate the starting locations for matching full radius and arc in motions.
l Calculate the coordinate location of a hole in a bolt-hole pattern.
Figure 1. Face milling operations require
calculations to find the X- and Y-axis positions
for each facing pass.
Figure 2. Hole-making operations such as
drilling require calculations to find the total
depth of the drill.
Lesson: 2/17
The Purpose of Toolpath Calculations
A key step during the development of a CNC part program is calculating the movements of every
tool. Creating accurate parts requires the careful tracking of each toolpath from one operation to
the next. A toolpath is the series of coordinate locations that indicate where a particular tool must
move during the machining of the part.
Every toolpath consists of a series of individual linear or circular movements. The programmer finds
the start and end locations for each of these movements in the coordinate system. Most often,
the programmer must track the coordinate location of the tool’s center throughout its cutting
operation. To find these exact coordinate locations, programmers rely on geometry and
trigonometry to solve for missing variables. Figure 1 shows you the blueprint for a sample part.
Copyright
2015asTooling
U, LLC. All
Using
this©part
an example,
thisRights
classReserved.
will teach you common operations performed on the
machining center and the methods for calculating their toolpaths.
Lesson: 2/17
The Purpose of Toolpath Calculations
A key step during the development of a CNC part program is calculating the movements of every
tool. Creating accurate parts requires the careful tracking of each toolpath from one operation to
the next. A toolpath is the series of coordinate locations that indicate where a particular tool must
move during the machining of the part.
Every toolpath consists of a series of individual linear or circular movements. The programmer finds
the start and end locations for each of these movements in the coordinate system. Most often,
the programmer must track the coordinate location of the tool’s center throughout its cutting
operation. To find these exact coordinate locations, programmers rely on geometry and
trigonometry to solve for missing variables. Figure 1 shows you the blueprint for a sample part.
Using this part as an example, this class will teach you common operations performed on the
machining center and the methods for calculating their toolpaths.
Figure 1. The program for this sample part
requires a series of toolpath calculations.
Lesson: 3/17
Program Zero Location
The typical milling part is fairly straightforward, with straight edges, a number of drilled holes, and
possibly a pocket or slot. For example, the part shown in Figure 1 has many of the same features
found on a common milling part.
Before you can calculate the toolpaths for a part, you must determine the location of program
zero. Program zero is the origin located on the part that provides the reference point for
distances between part features and the center of the tool. On some parts, a programmer may
locate program zero on a corner, as you can see in Figure 2. However, symmetrical parts, such
as the sample part in Figure 3, are easiest to calculate by locating program zero in the part’s
center, level with the top surface. By locating program zero in the center, the programmer has a
“mirror image” of each side of the part, with opposite matching points that are the same distance
from the center.
Not all parts make it easy to calculate their toolpaths. Keep in mind that complex parts, especially
parts with three-dimensional contour features, require CAD/CAM software to determine the
toolpaths. Nevertheless, programmers must know the steps for manually calculating the toolpaths
for common milling parts.
Copyright © 2015 Tooling U, LLC. All Rights Reserved.
Figure 1. The part has many common features
found on other parts machined on the mill.
Lesson: 3/17
Program Zero Location
The typical milling part is fairly straightforward, with straight edges, a number of drilled holes, and
possibly a pocket or slot. For example, the part shown in Figure 1 has many of the same features
found on a common milling part.
Before you can calculate the toolpaths for a part, you must determine the location of program
zero. Program zero is the origin located on the part that provides the reference point for
distances between part features and the center of the tool. On some parts, a programmer may
locate program zero on a corner, as you can see in Figure 2. However, symmetrical parts, such
as the sample part in Figure 3, are easiest to calculate by locating program zero in the part’s
center, level with the top surface. By locating program zero in the center, the programmer has a
“mirror image” of each side of the part, with opposite matching points that are the same distance
from the center.
Not all parts make it easy to calculate their toolpaths. Keep in mind that complex parts, especially
parts with three-dimensional contour features, require CAD/CAM software to determine the
toolpaths. Nevertheless, programmers must know the steps for manually calculating the toolpaths
for common milling parts.
Figure 1. The part has many common features
found on other parts machined on the mill.
Figure 2. Many parts on the mill have program
zero located in a corner.
Figure 3. Program zero is often located in the
center of symmetrical parts.
Copyright © 2015 Tooling U, LLC. All Rights Reserved.
Lesson: 4/17
Face Milling Calculations
Many milling parts start with a face milling operation that cuts across the entire top surface of the
part. The face milling operation creates a flat, horizontal surface that is precisely located on the Zaxis at Z=0. Depending on the part and the cutting tool, a face milling operation may require more
than one pass of the tool.
During face milling, the programmer must consider how much material to remove with each pass of
the tool. As you can see in Figure 1, 75% to 80% of the cutter’s diameter should be engaged in
the cut. The rest of the space is necessary for proper tooth and chip clearance. The portion of the
cutter engaged in the cut is called the step-over.
To determine the number of passes, the programmer must first select the specific milling cutter.
The programmer then finds the proper step-over for the cutting tool by calculating 75% or 80% of
the tool’s diameter. By comparing the size of the part and the size of the cutter’s step-over, the
programmer quickly determines how many passes are necessary to face the entire surface of the
part. Figure 2 compares how two different cutter diameters affect the number of facing passes.
Figure 1. Only 75% to 80% of a face mill’s
diameter should be engaged in the cut.
Figure 2. The diameter of the cutter
determines how many facing passes are
necessary.
Lesson: 5/17
The Face Milling Toolpath: Y-Axis
Consider a sample square part with 4.00 in. sides. Program zero is located in the center. How many
passes are necessary with a 2.48 in. diameter milling cutter? What are the coordinate locations for
each cutting pass?
First, you must calculate the cutter’s step-over, which is 75% to 80% of the cutter’s diameter. As
you can see in Figure 1, 75% of a 2.48 in. diameter cutter provides you with a 1.86 in. step-over.
Because the part is 4 in. on each side, the step-over covers less than half of the workpiece surface.
Therefore, three passes are necessary to cover the entire surface of the part.
Each pass travels horizontally at three different locations on the Y-axis. Find the value of Y for
each
face ©
milling
pass. In
toRights
use step-over
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2015 Tooling
U, order
LLC. All
Reserved.and engage only 75% of the cutter, the first
cutting pass must be along the edge of the workpiece. Keep in mind that the part program tracks
the cutter’s center relative to part zero. In this case, part zero is the horizontal centerline of the
workpiece, or exactly 2.00 in. between the part edges in the Y-axis. Subtract the step-over from
Lesson: 4/17
Face Milling Calculations
Many milling parts start with a face milling operation that cuts across the entire top surface of the
part. The face milling operation creates a flat, horizontal surface that is precisely located on the Zaxis at Z=0. Depending on the part and the cutting tool, a face milling operation may require more
than one pass of the tool.
During face milling, the programmer must consider how much material to remove with each pass of
the tool. As you can see in Figure 1, 75% to 80% of the cutter’s diameter should be engaged in
the cut. The rest of the space is necessary for proper tooth and chip clearance. The portion of the
cutter engaged in the cut is called the step-over.
To determine the number of passes, the programmer must first select the specific milling cutter.
The programmer then finds the proper step-over for the cutting tool by calculating 75% or 80% of
the tool’s diameter. By comparing the size of the part and the size of the cutter’s step-over, the
programmer quickly determines how many passes are necessary to face the entire surface of the
part. Figure 2 compares how two different cutter diameters affect the number of facing passes.
Figure 1. Only 75% to 80% of a face mill’s
diameter should be engaged in the cut.
Figure 2. The diameter of the cutter
determines how many facing passes are
necessary.
Lesson: 5/17
The Face Milling Toolpath: Y-Axis
Consider a sample square part with 4.00 in. sides. Program zero is located in the center. How many
passes are necessary with a 2.48 in. diameter milling cutter? What are the coordinate locations for
each cutting pass?
First, you must calculate the cutter’s step-over, which is 75% to 80% of the cutter’s diameter. As
you can see in Figure 1, 75% of a 2.48 in. diameter cutter provides you with a 1.86 in. step-over.
Because the part is 4 in. on each side, the step-over covers less than half of the workpiece surface.
Therefore, three passes are necessary to cover the entire surface of the part.
Each pass travels horizontally at three different locations on the Y-axis. Find the value of Y for
each face milling pass. In order to use step-over and engage only 75% of the cutter, the first
Copyright
© 2015
Tooling
U, LLC.
Rights
Reserved.
cutting
pass
must
be along
the All
edge
of the
workpiece. Keep in mind that the part program tracks
the cutter’s center relative to part zero. In this case, part zero is the horizontal centerline of the
workpiece, or exactly 2.00 in. between the part edges in the Y-axis. Subtract the step-over from
Figure 1. The cutter’s diameter and its step-
Lesson: 5/17
The Face Milling Toolpath: Y-Axis
Consider a sample square part with 4.00 in. sides. Program zero is located in the center. How many
passes are necessary with a 2.48 in. diameter milling cutter? What are the coordinate locations for
each cutting pass?
First, you must calculate the cutter’s step-over, which is 75% to 80% of the cutter’s diameter. As
you can see in Figure 1, 75% of a 2.48 in. diameter cutter provides you with a 1.86 in. step-over.
Because the part is 4 in. on each side, the step-over covers less than half of the workpiece surface.
Therefore, three passes are necessary to cover the entire surface of the part.
Each pass travels horizontally at three different locations on the Y-axis. Find the value of Y for
each face milling pass. In order to use step-over and engage only 75% of the cutter, the first
cutting pass must be along the edge of the workpiece. Keep in mind that the part program tracks
the cutter’s center relative to part zero. In this case, part zero is the horizontal centerline of the
workpiece, or exactly 2.00 in. between the part edges in the Y-axis. Subtract the step-over from
this 2.00 in. dimension (2.00 – 1.86) to find that the location of the cutter edge during the first
cutting pass is Y = 0.14. The radius of the cutting tool extends from its edge to its center, so use
the cutter radius to find the programmable Y-axis value. If you divide the milling cutter’s diameter
(2.48 in.) by 2, you find that the tool radius is 1.24 inches. Add the tool radius to the tool edge
location (1.24 + 0.14) to find that Y=1.38 for the first pass. For the second cutting pass, simply
repeat the first pass on the opposite, or negative, side of the part centerline. Therefore, the value
for the second pass is Y=-1.38.
Figure 1. The cutter’s diameter and its stepover.
The first two 1.86 in. cutting passes leave a 0.28 in. band of uncut material in the center of the
workpiece. However, programming the final cutting pass at 0.00 on the Y-axis engages only those
teeth directly on the face mill’s centerline and can lead to instability of the cutting tool. You should
program the final pass so that the remaining material is between the centerline and the edge of the
tool. Entering a value of Y=-1.00 is ideal. Figure 2 shows the Y-axis values for all three cutting
passes. Since the radius of the cutter is 1.24 in., this value places the edge of the cutter at
Y=0.24, which provides the tool 0.10 in. of clearance past the edge of the uncut material.
Figure 2. The Y-axis locations for the cutter’s
center at each facing pass.
Figure 3. The toolpath calculations as they
appear in the actual program codes.
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Lesson: 6/17
Lesson: 6/17
The Face Milling Toolpath: X-Axis
Once you determine where these three face milling passes take place on the Y-axis, you can find
the values of the start and end of the cuts on the X-axis. Each face milling pass starts at the same
location on the X-axis. For this sample part, program zero is located in the center. Therefore, Xaxis values left of the center are negative. Because the part is 4 in. wide, X equals -2.000 on the
left edge and 2.000 on the right edge.
As you can see in Figure 1, the starting distance from the part’s edge must include the cutter’s
radius and an approach distance. The typical approach distance is between 0.100 and 0.150
inches. The radius of the cutter is half its diameter, which is 1.24 inches. Because the tool is left of
the part’s edge, you subtract the radius (-1.240) and approach (-0.150) from X=-2.000 on the left
edge. Consequently, the center of the tool is located at X=-3.39 at the start of all three cuts, as
shown in Figure 2.
Like the starting location, the end of the face milling pass must account for the cutter’s radius and
a 0.150 in. clearance distance between the tool and part. Keep in mind that program zero is in the
part’s center. If X=-3.39 at the start of the cut, X=3.39 at the end. Figure 3 shows where these
values appear in the actual program codes.
Figure 1. The X-axis starting location includes
the cutter’s radius and an approach distance.
Figure 2. The start and end of each milling
pass share the same X -axis value.
Figure 3. The toolpath calculations as they
appear in the actual program codes.
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Lesson: 7/17
Pocket Milling Calculations
Many milling parts require a recessed pocket. Pocket milling is often done with an end mill, which
has a smaller diameter than a face mill. Unlike the typical facing operation with its simple,
horizontal cutting movements, pocket milling requires a boxing routine. As you can see in Figure
1, a boxing routine starts in the center of the pocket and gradually enlarges the hole by cutting a
series of widening rectangular movements.
Theoretically, you should be able to use a step-over that is 75% of the end mill’s diameter.
However, a tool’s length-to-diameter ratio may require you to reduce the step-over. An end mill
that extends more than three times its diameter from the toolholder may experience deflection.
By reducing the step-over for an end mill, you can reduce deflection and improve surface finish.
Pockets typically have rounded corners. As you can see in Figure 2, the size of the radius in each
corner limits the size of the end mill that you use. You cannot use an end mill with a radius larger
than the corner radius. However, you want to use as large of an end mill as possible to take larger
cuts and improve rigidity.
Programmers often leave a small amount of material on the walls or bottom of the pocket for a final
finishing pass. This amount may be anywhere from 0.005 to 0.015 in. of material, depending on
the size of the end mill. A finishing pass cleans up the pocket and leaves a good surface finish.
Figure 1. A boxing routine consists of a series
of widening rectangular tool movements.
Figure 2. The corner radius of a pocket limits
the size of the end mill.
Lesson: 8/17
The Pocket Toolpath
The pocket in the sample part is 3 in. wide in each direction and 0.375 in. deep. The pocket also
has a 0.5 in. radius in each corner. If you have a 0.5 in. diameter end mill, how would you find the
coordinates to create the pocket?
Figure 1 shows the first few linear tool movements. The first motion is to feed the end mill vertically
into
the center
program
zero.
end mill moves up in the pocket to Y=0.25, which is a
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© 2015atTooling
U, LLC.
AllNext,
Rightsthe
Reserved.
50% step-over compared to the end mill’s diameter. The cutter then moves left until X=-0.25,
down until Y=-0.25, right until X=0.25, and up until Y=0.50 inches. These individual movements
Lesson: 7/17
Pocket Milling Calculations
Many milling parts require a recessed pocket. Pocket milling is often done with an end mill, which
has a smaller diameter than a face mill. Unlike the typical facing operation with its simple,
horizontal cutting movements, pocket milling requires a boxing routine. As you can see in Figure
1, a boxing routine starts in the center of the pocket and gradually enlarges the hole by cutting a
series of widening rectangular movements.
Theoretically, you should be able to use a step-over that is 75% of the end mill’s diameter.
However, a tool’s length-to-diameter ratio may require you to reduce the step-over. An end mill
that extends more than three times its diameter from the toolholder may experience deflection.
By reducing the step-over for an end mill, you can reduce deflection and improve surface finish.
Pockets typically have rounded corners. As you can see in Figure 2, the size of the radius in each
corner limits the size of the end mill that you use. You cannot use an end mill with a radius larger
than the corner radius. However, you want to use as large of an end mill as possible to take larger
cuts and improve rigidity.
Programmers often leave a small amount of material on the walls or bottom of the pocket for a final
finishing pass. This amount may be anywhere from 0.005 to 0.015 in. of material, depending on
the size of the end mill. A finishing pass cleans up the pocket and leaves a good surface finish.
Figure 1. A boxing routine consists of a series
of widening rectangular tool movements.
Figure 2. The corner radius of a pocket limits
the size of the end mill.
Lesson: 8/17
The Pocket Toolpath
The pocket in the sample part is 3 in. wide in each direction and 0.375 in. deep. The pocket also
has a 0.5 in. radius in each corner. If you have a 0.5 in. diameter end mill, how would you find the
coordinates to create the pocket?
Figure 1 shows the first few linear tool movements. The first motion is to feed the end mill vertically
into the center at program zero. Next, the end mill moves up in the pocket to Y=0.25, which is a
Copyright
© 2015compared
Tooling U, to
LLC.
Rights
Reserved.
50%
step-over
theAllend
mill’s
diameter. The cutter then moves left until X=-0.25,
down until Y=-0.25, right until X=0.25, and up until Y=0.50 inches. These individual movements
follow a counterclockwise rectangular pattern that begins the pocket.
Lesson: 8/17
The Pocket Toolpath
The pocket in the sample part is 3 in. wide in each direction and 0.375 in. deep. The pocket also
has a 0.5 in. radius in each corner. If you have a 0.5 in. diameter end mill, how would you find the
coordinates to create the pocket?
Figure 1 shows the first few linear tool movements. The first motion is to feed the end mill vertically
into the center at program zero. Next, the end mill moves up in the pocket to Y=0.25, which is a
50% step-over compared to the end mill’s diameter. The cutter then moves left until X=-0.25,
down until Y=-0.25, right until X=0.25, and up until Y=0.50 inches. These individual movements
follow a counterclockwise rectangular pattern that begins the pocket.
To widen the pocket, you repeat this process in 0.25 in. increments until you approach the final
size of the pocket. This is your boxing routine. All of these movements are linear movements,
except for the outermost pass. To add each corner radius, you alternate between linear and
counterclockwise circular cuts.
Figure 2 shows the stock that is left for finishing. The finishing pass removes the small amount of
stock left after roughing. In Figure 3, you can see that the programmed radius is 0.24 inches. The
part requires a 0.5 in. radius, but you must subtract the radius of the cutter (0.25 in.) and an
appropriate finishing stock (0.01 in.). To leave finishing stock, calculate an imaginary boundary
0.01 inches inside the pocket. The final finishing pass repeats these movements, except the radius
is now 0.25 in. to remove the finishing stock and complete the pocket.
Figure 1. The first few linear movements begin
the boxing routine.
Figure 2. The red line indicates the finishing
stock that is intentionally left for a final
finishing pass.
Copyright © 2015 Tooling U, LLC. All Rights Reserved.
finishing pass.
Figure 3. The toolpath calculations as they
appear in the actual program codes.
Lesson: 9/17
Spot Drilling Calculations
Almost every milling part involves hole-making operations. The first tool used to machine a hole is
the spot drill. The spot drill is a short, sturdy drill used to start a hole. The spot drill ensures that
the drill following it creates a hole that is accurately located.
The CNC control tracks the position of the spot drill by its tip. As a programmer, you have to
calculate how far the tip must enter the surface to start the hole properly. The typical spot drill has
a 90° tip. As you can see in Figure 1, this tip makes it easy to calculate the spot drill’s depth.
Because the 90° tip forms a 45° right triangle, the distance that the tip enters the surface is the same as the radius of the hole formed by the spot drill. If you divide your hole diameter by 2, you
find the necessary depth for the spot drill.
Programmers often use a spot drill that is wider than the eventual hole. The programmer then
calculates a depth that is 0.02 to 0.03 in. larger than the hole diameter. Consider the hole in Figure
2. Because the spot drill has a larger diameter than the drill used to make the hole, this extra
distance leaves a chamfer around the edge after the hole is drilled. The size of the chamfer is half
the extra distance added to the spot drill’s depth.
Figure 1. The distance that the tip enters the
surface equals the radius of the hole that is
formed.
Copyright © 2015 Tooling U, LLC. All Rights Reserved.
Figure 2. By programming an extra distance, a
chamfer is left around the hole after it is drilled.
Lesson: 9/17
Spot Drilling Calculations
Almost every milling part involves hole-making operations. The first tool used to machine a hole is
the spot drill. The spot drill is a short, sturdy drill used to start a hole. The spot drill ensures that
the drill following it creates a hole that is accurately located.
The CNC control tracks the position of the spot drill by its tip. As a programmer, you have to
calculate how far the tip must enter the surface to start the hole properly. The typical spot drill has
a 90° tip. As you can see in Figure 1, this tip makes it easy to calculate the spot drill’s depth.
Because the 90° tip forms a 45° right triangle, the distance that the tip enters the surface is the same as the radius of the hole formed by the spot drill. If you divide your hole diameter by 2, you
find the necessary depth for the spot drill.
Programmers often use a spot drill that is wider than the eventual hole. The programmer then
calculates a depth that is 0.02 to 0.03 in. larger than the hole diameter. Consider the hole in Figure
2. Because the spot drill has a larger diameter than the drill used to make the hole, this extra
distance leaves a chamfer around the edge after the hole is drilled. The size of the chamfer is half
the extra distance added to the spot drill’s depth.
Figure 1. The distance that the tip enters the
surface equals the radius of the hole that is
formed.
Figure 2. By programming an extra distance, a
chamfer is left around the hole after it is drilled.
Lesson: 10/17
The Spot Drill Toolpath
For the sample part, the 0.500 in. diameter holes in each pocket corner require spot drilling. The
pocket is 0.375 in. deep. If you want to leave a 0.015 in. chamfer around each hole, what depth do
you need for a 90° spot drill 0.625 inches in diameter?
Because the spot drill diameter is larger than the hole, it can leave a chamfer after the hole is
drilled, as shown in Figure 1. The spot drill must enter the surface until it reaches a distance 0.5 in.
across its diameter, plus an extra 0.030 in. to account for the chamfer. The extra 0.030 inches will
leave a 0.015 in. chamfer around the hole. By adding the hole diameter (0.500) and the extra
chamfer (0.030), you find that the spot drill must penetrate the part until it reaches 0.530 in.
across its diameter.
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The 90° tip creates a 45° right triangle. The required depth is half the distance across the spot drill’s diameter. If you divide the diameter distance (0.530) by two, you find that the required depth
is 0.265 inches.
Lesson: 10/17
The Spot Drill Toolpath
For the sample part, the 0.500 in. diameter holes in each pocket corner require spot drilling. The
pocket is 0.375 in. deep. If you want to leave a 0.015 in. chamfer around each hole, what depth do
you need for a 90° spot drill 0.625 inches in diameter?
Because the spot drill diameter is larger than the hole, it can leave a chamfer after the hole is
drilled, as shown in Figure 1. The spot drill must enter the surface until it reaches a distance 0.5 in.
across its diameter, plus an extra 0.030 in. to account for the chamfer. The extra 0.030 inches will
leave a 0.015 in. chamfer around the hole. By adding the hole diameter (0.500) and the extra
chamfer (0.030), you find that the spot drill must penetrate the part until it reaches 0.530 in.
across its diameter.
The 90° tip creates a 45° right triangle. The required depth is half the distance across the spot drill’s diameter. If you divide the diameter distance (0.530) by two, you find that the required depth
is 0.265 inches.
Now you must find this depth on the Z-axis. As you can see in Figure 2, The origin is located on
the top surface of the part where Z=0, and negative directions travel into the part. Because the
pocket is 0.375 in. deep, Z=-0.375 on the pocket’s surface. By subtracting the spot drill’s depth (0.265) from the pocket surface (-0.375), you find that Z=-0.640 at the spot drill’s final depth.
Figure 3 shows where these Z values appear in the actual program codes.
Figure 1. An additional 0.030 in. leaves a
0.015 in. chamfer on the hole.
Figure 2. Z=0 at the top surface of the part.
Figure 3. The total depth of the spot drill
appears in the actual program codes.
Lesson: 11/17
Drilling Calculations
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Drilling operations follow spot drilling. Like spot drilling calculations, drilling requires that you
determine the final depth for the drill point. However, there are two key differences. The typical drill
has a 118° tip, which makes calculations more difficult. Also, when drilling through holes, the drill Lesson: 11/17
Drilling Calculations
Drilling operations follow spot drilling. Like spot drilling calculations, drilling requires that you
determine the final depth for the drill point. However, there are two key differences. The typical drill
has a 118° tip, which makes calculations more difficult. Also, when drilling through holes, the drill has to completely penetrate the workpiece to create the hole.
As you can see in Figure 1, the final depth of the drill includes the depth of the hole, the length of
the drill tip, and a small amount of clearance. This clearance is normally between 0.03 to 0.05
inches, and it ensures that the hole is completely drilled through.
To find the length of the tip, programmers have to use some trigonometry. In Figure 2, you can
see that the drill’s centerline divides the tip into two equal 59° angles. One side of the triangle is the length of the drill’s radius. If you divide the drill’s radius by the tangent of 59°, you find the length of the drill tip.
Figure 1. The total drill depth equals the hole
depth, the drill tip length, and a small
clearance.
Figure 2. The centerline of the drill divides its
tip into two equal 59° angles.
Lesson: 12/17
The Drilling Toolpath
After spot drilling the sample part, you are ready to drill the 0.5 in. diameter hole in each corner
with a 118° twist drill. If the part is 0.75 in. thick, what is the total depth that the drill tip travels?
Figure 1 shows the total depth of the drill. The total drill depth includes the hole depth, the drill
tip’s length, and some extra clearance. To find the hole depth, consider the location of program
zero. For the sample part, program zero is located on the top surface, where Z=0. You know that
the part is 0.75 in. thick and that each hole completely penetrates the part. Consequently, Z=-0.75
at the bottom of the hole.
A 0.5 in. diameter hole requires a 0.5 in. diameter drill. To find the drill tip length, you can calculate
the right triangle formed by the drill’s centerline, its angled tip, and its radius. As you can see in
Figure 2, the centerline divides the tip into two 59° angles. The radius of the drill is half its diameter, which is 0.25 inches. If you divide the drill’s radius (0.250) by the tangent of 59° (1.664),
you find that the length of the drill tip is approximately 0.150 inches.
Now you have all the information you need to find the drill’s final depth. Tool movements into the
part are negative on the Z-axis. You know that Z=-0.75 at the hole’s bottom. If you subtract the
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drill tip length (-0.150) and a slight clearance (-0.050), you find that Z=-0.950 to reach the drill’s
total depth. Figure 3 shows where these values appear in the actual program codes.
Figure 1. The total drill depth equals the hole
depth, the drill tip length, and a small
clearance.
Lesson: 12/17
The Drilling Toolpath
After spot drilling the sample part, you are ready to drill the 0.5 in. diameter hole in each corner
with a 118° twist drill. If the part is 0.75 in. thick, what is the total depth that the drill tip travels?
Figure 1 shows the total depth of the drill. The total drill depth includes the hole depth, the drill
tip’s length, and some extra clearance. To find the hole depth, consider the location of program
zero. For the sample part, program zero is located on the top surface, where Z=0. You know that
the part is 0.75 in. thick and that each hole completely penetrates the part. Consequently, Z=-0.75
at the bottom of the hole.
A 0.5 in. diameter hole requires a 0.5 in. diameter drill. To find the drill tip length, you can calculate
the right triangle formed by the drill’s centerline, its angled tip, and its radius. As you can see in
Figure 2, the centerline divides the tip into two 59° angles. The radius of the drill is half its diameter, which is 0.25 inches. If you divide the drill’s radius (0.250) by the tangent of 59° (1.664),
you find that the length of the drill tip is approximately 0.150 inches.
Figure 1. The total drill depth equals the hole
depth, the drill tip length, and a small
clearance.
Now you have all the information you need to find the drill’s final depth. Tool movements into the
part are negative on the Z-axis. You know that Z=-0.75 at the hole’s bottom. If you subtract the
drill tip length (-0.150) and a slight clearance (-0.050), you find that Z=-0.950 to reach the drill’s
total depth. Figure 3 shows where these values appear in the actual program codes.
Figure 2. Using trig, you find that the drill tip
length is 0.150 inches.
Figure 3. The drill's final depth appears in the
actual program codes.
Lesson: 13/17
CRC on the Mill
Most mill controls have cutter radius compensation (CRC). CRC is an offset that adjusts for the
radius of the tool, and it is only necessary for tools that travel in the X- or Y-axes. Instead of
calculating the toolpath to the center of the tool, the programmer enters a toolpath that follows
the contour of the part. The control compensates for the radius of the tool. The programmer adds
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either
a G41
or G42
to the
program
to tell
the control what direction to compensate for the tool
radius. When viewed in the direction of travel, G41 indicates that the tool is moving on the lefthand side of the part, and G42 indicates the tool is on the right-hand side.
Lesson: 13/17
CRC on the Mill
Most mill controls have cutter radius compensation (CRC). CRC is an offset that adjusts for the
radius of the tool, and it is only necessary for tools that travel in the X- or Y-axes. Instead of
calculating the toolpath to the center of the tool, the programmer enters a toolpath that follows
the contour of the part. The control compensates for the radius of the tool. The programmer adds
either a G41 or G42 to the program to tell the control what direction to compensate for the tool
radius. When viewed in the direction of travel, G41 indicates that the tool is moving on the lefthand side of the part, and G42 indicates the tool is on the right-hand side.
As you can see in Figure 1, CRC poses some programming challenges because it requires a
ramping motion every time that this compensation is initiated. The ramping motion must be
longer than the cutting tool’s radius. Depending on the size of the tool, ramping motions can be
quite long and cumbersome. The larger the tool, the larger the ramping motion.
To strike a balance, programmers may include G41 codes in the program but enter toolpaths that
track the center of the cutter. Figure 2 shows a toolpath that factors in the cutter’s radius. The
operator enters “0.0” as the cutter’s radius in the offset table. With this method, the programmer
commits to using a particular tool diameter. You must choose a particular tool for each operation,
and you can’t change it without changing the program. However, CRC becomes essentially a wear
offset that the operator can adjust to fine-tune the program. Fortunately, most CAD/CAM
software lets you choose how you want to use CRC in the program.
Figure 1. G41 and G42 compensate the tool to
the left or right in the direction of the
programmed toolpath.
Figure 2. Without CRC, the programmer must
calculate toolpaths that follow the cutter ’s
center.
Lesson: 14/17
Full-Circle Milling Calculations
Along with a rectangular pocket with rounded corners, common milling features include circular
pockets and larger holes that require circular milling. These features require programming full-circle
movements.
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As
you can
FigureU,1,LLC.
partial
arcs often
use the radius method to program a circular motion.
However, full-circle motions are best done with the arc center method, which uses an I code
and/or J code. These codes indicate an incremental distance between the starting point and the
Lesson: 14/17
Full-Circle Milling Calculations
Along with a rectangular pocket with rounded corners, common milling features include circular
pockets and larger holes that require circular milling. These features require programming full-circle
movements.
As you can see in Figure 1, partial arcs often use the radius method to program a circular motion.
However, full-circle motions are best done with the arc center method, which uses an I code
and/or J code. These codes indicate an incremental distance between the starting point and the
arc’s center. For example, the program block G03J-0.24 says, “take a full-circle counterclockwise
cut using an arc center that is –0.24 inches below the starting point.”
Full-circle pockets or holes often include an arc-in motion and arc-out motion, as shown in Figure
2. While it is possible to plunge straight into a full-circle cut, this movement tends to leave a mark.
Arcing in and arcing out leaves a smooth, well-blended surface on the part. A programmer uses an
R code and the radius method for these arc-in and arc-out motions.
Figure 1. Partial arcs use an R code; Full arcs
use I/J codes.
Figure 2. Arc in and arc out motions leave a
smooth surface on the hole.
Lesson: 15/17
The Full Circle Toolpath
In the sample part, the spot drill and drill started the hole in the center. Now you must use a 0.500
in. diameter end mill to widen the hole and create a 1.000 in. diameter. Program zero is located on
the center of the hole. How do you determine the correct tool motions?
First, the end mill drops down 0.100 in. below the bottom of the hole. Because Z=-0.75 at the hole
bottom, the end mill drops until Z=-0.85 inches. An end mill has a flat bottom, so there is no need
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to
account©for
a drill
point.
Before you begin your full-circle cut, you must first determine where your arc-in motion will blend
Lesson: 15/17
The Full Circle Toolpath
In the sample part, the spot drill and drill started the hole in the center. Now you must use a 0.500
in. diameter end mill to widen the hole and create a 1.000 in. diameter. Program zero is located on
the center of the hole. How do you determine the correct tool motions?
First, the end mill drops down 0.100 in. below the bottom of the hole. Because Z=-0.75 at the hole
bottom, the end mill drops until Z=-0.85 inches. An end mill has a flat bottom, so there is no need
to account for a drill point.
Before you begin your full-circle cut, you must first determine where your arc-in motion will blend
into the larger full circle. The radius of the hole is 0.500 inches. You must subtract the end mill’s
radius (0.250) from the hole’s radius (0.500) to find Y at this blending point. In Figure 1, you see
that this takes place at X=0 and Y=0.250 so that the edge of the end mill meets the boundary of
the hole.
To start the cut, the mill moves up until Y=0.24 inches. Then the tool completes a full circle, which
roughs out the hole. After roughing the hole, the mill drops down and to the right until X=0.125
and Y=0.125 inches. This is the starting point for arc-in motion. As you can see in Figure 2, a good
starting location is about half the length of the radius used in the full-circle motion. You use an R
code to program the arc in, with the blending point as the end point of the arc.
Figure 1. The blending point is the hole ’s
radius minus the cutter’s radius.
After arcing in, the end mill begins the full-circle motion. A single J code initiates a full-circle motion
with a 0.25 in. radius. For the arc-out motion, you program a mirror image of the arc in. The
starting point for arcing out is the blending point, and the ending point is located at X=-0.125 and
Y=0.125 inches. Figure 3 shows where all these calculations appear in the actual program codes.
Figure 2. The radius for the arc-in motion is
half the radius of the full-circle motion.
Figure 3. The toolpath calculations as they
appear in the actual program codes.
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Lesson: 16/17
The Bolt Hole Pattern
Hole making on the mill often involves a sequence of operations. For example, the sample part
has six smaller holes around the center hole that are spot drilled, drilled, and then tapped.
These six holes form a bolt-hole pattern, as shown in Figure 1. To program these holes, you
must find the location of their centers on the X- and Y-axes.
Because spot drills, drills, and taps cut only on the Z-axis, you program to the tool and the hole
center. The six bolt holes form a 360° circle. The blueprint specifies the diameter of this circle, which is 1.500 inches. Two holes are located top and bottom exactly on the Y-axis. The
distance to each hole is the radius of the circle. Consequently, X=0 and Y=0.75 for the top hole,
and X=0 and Y=-0.75 at the bottom.
To find the other hole locations, you can use some trigonometry calculations. As you can see in
Figure 2, the six holes divide the circle into six 60° angles. If you draw lines back to the X- and
Y-axis from the center of a hole, you form a right triangle with the 0.75 in. radius as the
hypotenuse. If you multiply the sine of 60° (0.866); by the radius (0.750), you find that the distance on the X-axis is about 0.650 inches. Likewise, the cosine of 60° (0.500) multiplied by the radius (0.750) gives you a distance of 0.375 inches on the Y-axis. Because program zero is
located in the center, all of these holes have coordinates that are mirror images of each other.
Figure 3 shows where these values appear in the actual program codes.
Figure 1. A bolt-hole pattern consists of individual
holes positioned around an imaginary circle.
Figure 2. The radius of the bolt -hole circle forms a
right triangle that helps you find the location of the
holes.
Figure 3. The toolpath calculations as they appear
in the actual program codes.
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Lesson: 17/17
Summary
Milling programs require calculations to determine the toolpaths used to machine the part. Each
toolpath consists of a series of coordinate locations that determine the tool’s distance from
program zero. While some programmers may locate program zero in the corner of a part,
symmetrical parts often locate program zero in the center.
Many milling programs begin with face milling. The step-over for a face mill is 75% to 80% of the
face mill’s diameter. This distance determines how many passes are necessary to face the entire
part surface. Many parts also require pocket milling, which uses a boxing routine to gradually
enlarge the pocket. Most pockets have a corner radius, which limits the size of the end mill that can
be used.
Hole-making operations require calculations to find the depth of the tool tip. When spot drilling,
programmers will add an extra distance to the depth. This leaves a chamfer around the hole after it
is drilled. To find the total depth for drilling, programmers calculate the hole depth, the drill tip
length, and then add a slight clearance beyond the bottom of the hole.
Figure 1. Only 75% to 80% of a face mill’s
diameter should be engaged in the cut.
Full-circle milling requires arc-in and arc-out motions, which are partial arc motions into and out of
the full-circle motion that leave a smooth finish. Partial arc motions use an R code to determine the
radius, while full-arc motions use I or J codes. Many parts also have bolt-hole circle patterns. By
using trigonometry, a programmer can determine the center location for each hole in the pattern.
Figure 2. The corner radius of a pocket limits
the size of the end mill.
Figure 3. The distance that the tip enters the
surface equals the radius of the hole that is
formed.
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Class Vocabulary
Term
Definition
Approach
Arc Center Method
A slight distance added to a toolpath at the beginning of a cut for safety reasons.
A method for programming circular tool movements that requires an I code and J code to indicate the
location of the arc's center along the X- and Y-axes. The arc center method is best used for full-arc
motions.
Arc-In Motion
A partial-arc motion that leads into a larger arc motion. Arc in and arc out motions leave a smooth surface
finish.
Arc-Out Motion
A partial-arc motion that exits from a larger arc motion. Arc in and arc out motions leave a smooth surface
finish.
Bolt-Hole Pattern
Boxing Routine
CAD/CAM
Chamfer
Clearance
Contour Feature
Coordinate System
Cosine
Cutter Radius Compensation
Deflection
End Mill
Face Mill
Face Milling
Finishing Pass
Finishing Stock
Hypotenuse
A common specification on milled parts that requires a series of equally spaced holes around the
circumference of a larger imaginary circle.
A series of increasingly larger rectangular toolpaths used to machine a rectangular pocket.
Computer-aided design/computer-aided manufacturing. CAD/CAM is the use of software to aid in the
design and manufacturing of a part.
A small, angled surface added to an edge of a workpiece. A chamfer removes the sharp edge and helps
eliminate burrs.
Any useful space that is intentionally maintained between components.
A part feature that is non-linear, or curved.
The numerical system that describes the location of an object by numerically expressing its distance from a
fixed position along three linear axes. The coordinate system consists of the X-, Y-, and Z-axes.
In a right triangle, the ratio of the length of the side adjacent to the angle divided by the hypotenuse.
An offset used on the machining center that accounts for variations in tool diameter. CRC is only necessary
for tools that continuously cut along a horizontal plane.
The unintended movement or repositioning of a component due to a mechanical force. Deflection of a
cutting tool can cause poor surface finish and inaccurate dimensions.
A thin, tall mill cutter with a flat bottom and cutting edges that wind up the sides. Both the bottom and
side of the end mill provide cutting surfaces during milling operations.
A flat mill cutter with multiple cutting teeth surrounding the tool. The bottom of the face mill is primarily the
cutting surface during milling operations.
A milling operation in which the surface of the workpiece is perpendicular to the spindle axis. Face milling
primarily is used to mill the top surface of the part.
A final cutting pass that produces the necessary surface finish and brings a feature to its proper size.
The small amount of material that is intentionally left for a finishing pass.
In a right triangle, the side located opposite the right angle.
I Code
For circular interpolation, the program code that indicates the location of the arc's center along the X-axis.
I and J codes are used for the arc center method.
J Code
For circular interpolation, the program code that indicates the location of the arc's center along the Y-axis.
I and J codes are used for the arc center method.
Length-To-Diameter Ratio A ratio describing the length of a cylindrical tool or workpiece compared to its diameter. Higher length-todiameter
ratios offer less rigidity.
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Milling Cutter
Any multi-point tool that is used to remove metal from the surface of a workpiece.
I and J codes are used for the arc center method.
Length-To-Diameter Ratio
A ratio describing the length of a cylindrical tool or workpiece compared to its diameter. Higher length-todiameter ratios offer less rigidity.
Milling Cutter
Any multi-point tool that is used to remove metal from the surface of a workpiece.
Part Program
A series of instructions used by a CNC machine to perform the necessary sequence of operations to
machine a specific workpiece.
Pocket
An interior recess that is cut into the surface of a workpiece. Pockets may be round or rectangular.
Program Zero
The position that acts as the origin for the part program of a particular workpiece. This position is unique
to each workpiece design, and it is selected by the part programmer.
R Code
For circular interpolation, the program code that indicates the length of the arc's radius. In certain canned
cycles, an R code indicates the R level for tool return.
Radius Method
Ramping Motion
Sine
Spot Drill
Step-Over
Symmetrical Part
Tangent
Toolpath
Trigonometry
Wear Offset
A method for programming circular tool movements that requires an R code to indicate the size of the arc's
radius. The radius method is best used for partial-arc motions.
A linear motion of the tool that is required for a control to adjust for a particular tool offset.
In a right triangle, the ratio of the length of the side opposite the angle divided by the hypotenuse.
A short, sturdy drill used to start a hole and accurately locate it. Most spot drills have a 90° tip.
The size of the cutter's diameter that is engaged in a cut. The step-over should be 75% to 80% of the
cutter's diameter.
A part that can be divided by a line into two equal halves, with identical features that are equal distances
from the dividing line. Both sides appear as mirror images of each other.
In a right triangle, the ratio of the length of the side opposite the angle divided by the adjacent side.
The series of coordinate positions that determine the movement of a tool during a machining operation.
The branch of mathematics that addresses the measurements and relationships of a triangle and its parts.
An offset used on a turning center and some machining centers that allows for the slight adjustment of
tool tip location. Wear offsets account for part deflection, tool wear, etc.
X-Axis
On the mill, the linear axis representing coordinate positions along the longest distance parallel to the
worktable.
Y-Axis
On the mill, the linear axis representing coordinate positions along the shortest distance parallel to the
worktable.
Z-Axis
On the mill, the linear axis representing coordinate positions perpendicular to the worktable. The Z-axis is
always parallel to the spindle.
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