Cnc notes (1)

INTRODUCTION
Definition

Computer Numerical Control (CNC) is one in which the functions and motions of a machine
tool are controlled by means of a prepared program containing coded alphanumeric data.
CNC can control the motions of the workpiece or tool, the input parameters such as feed,
depth of cut, speed, and the functions such as turning spindle on/off, turning coolant on/off.

Applications

The applications of CNC include both for machine tool as well as non-machine tool areas.
In the machine tool category, CNC is widely used for lathe, drill press, milling machine,
grinding unit, laser, sheet-metal press working machine, tube bending machine etc. Highly
automated machine tools such as turning center and machining center which change the
cutting tools automatically under CNC control have been developed. In the non-machine tool
category, CNC applications include welding machines (arc and resistance), coordinate
measuring machine, electronic assembly, tape laying and filament winding machines for
composites etc.

Advantages and Limitations

The benefits of CNC are (1) high accuracy in manufacturing, (2) short production time, (3)
greater manufacturing flexibility, (4) simpler fixturing, (5) contour machining (2 to 5 -axis
machining), (6) reduced human error. The drawbacks include high cost, maintenance, and the
requirement of skilled part programmer .

ELEMENTS OF A CNC

A CNC system consists of three basic components (Figure 2) :

1. Part program
2. Machine Control Unit (MCU)
3. Machine tool (lathe, drill press, milling machine etc)

Part Program

The part program is a detailed set of commands to be followed by the machine tool. Each
command specifies a position in the Cartesian coordinate system (x,y,z) or motion (workpiece
travel or cutting tool travel), machining parameters and on/off function. Part programmers
should be well versed with machine tools, machining processes, effects of process variables,
and limitations of CNC controls. The part program is written manually or by using computer-
assisted language such as APT (Automated Programming Tool).

MACHINE TOOL

Figure 2. A typical numerical control system for a milling machine

Machine Control Unit

The machine control unit (MCU) is a microcomputer that stores the program and executes the
commands into actions by the machine tool. The MCU consists of two main units: the data
processing unit (DPU) and the control loops unit (CLU). The DPU software includes control
system software, calculation algorithms, translation software that converts the part program
into a usable format for the MCU, interpolation algorithm to achieve smooth motion of the
cutter, editing of part program (in case of errors and changes) . The DPU processes the data
from the part program and provides it to the CLU which operates the drives attached to the
machine leadscrews and receives feedback signals on the actual position and velocity of each
one of the axes. A driver (dc motor) and a feedback device are attached to the leadscrew.
The CLU consists of the circuits for position and velocity control loops, deceleration and
backlash take up, function controls such as spindle on/off.

Machine Tool

The machine tool could be one of the following: lathe, milling machine, laser, plasma,
coordinate measuring machine etc. Figure 3 shows that a right-hand coordinate system is used
to describe the motions of a machine tool . There are three linear axes (x,y,z), three rotational
axes (i,j,k), and other axes such as tilt (9) are possible. For example, a 5-axis machine
implies any combination of x,y,z, i,j,k,and 6.

Figure 3 . Right-hand coordinate system used in drill press and lathe

5

PRINCIPLES OF CNC

Basic Length Unit (BLU)

Each BLU unit corresponds to the position resolution of the axis of motion. For example,
1 BLU = 0.0001" means that the axis will move 0.0001" for every one electrical pulse
received by the motor . The BLU is also referred to as Bit (binary digit).

Pulse = BLU = Bit

Point-to-Point Systems

Point-to-point systems are those that move the tool or the workpiece from one point to
another and then the tool performs the required task. Upon completion, the tool (or
workpiece) moves to the next position and the cycle is repeated (Figure 4). The simplest
example for this type of system is a drilling machine where the workpiece moves .

In this system, the feed rate and the path of the cutting tool (or workpiece) have no
significance on the machining process . The accuracy of positioning depends on the system's
resolution in terms of BLU (basic length unit) which is generally between 0 .001" and 0.0001" .

Workpiece

Figure 4. Cutter path between holes in a point-to-point system

Example 1

The XY table of a drilling machine has to be moved from the point (1,1) to the point
(6,3). Each axis can move at a velocity of 0.5"/sec, and the BLU is 0.0001", find the
travel time and resolution.

Travel time in X-axis is (6-1)/0 .5 = 10 sec, in Y-axis is (3-1)/0 .5= 4 sec .
Travel time = 10 sec
Resolution = BLU = 0.0001

Continuous Path Systems (Straight cut and Contouring systems)

These systems provide continuous path such that the tool can perform while the axes are
moving, enabling the system to generate angular surfaces, two-dimensional curves, or three-
dimensional contours . Example is a milling machine where such tasks are accomplished
(Figure 5). Each axis might move continuously at a different velocity. Velocity error is
significant in affecting the positions of the cutter (Figure 5). It is much more important in
circular contour cutting where one axis follows sine function while the other follows cosine
function. Figure 6 illustrates point-to-point and continuous path for various machines .

Figure 5. (a) Continuous path cutting and (b) Position error caused by the velocity error

Example 2

A CNC milling machine has to cut a slot located between the points (0,0) and (4,3)
on the XY-plane where the dimensions are in inches. If the speed along the slot is to
be 0.1 in/sec, find the cutting time and axial velocities.

Distance traveled along the slot = (16+9)'"2 = 5"

Cutting time = 5/0.1 = 50 sec

Vx = xV/(x2+y2)" = 4(0.1)/5 = 0.08 in/sec
Vy =yV/(x2+y2)'"2 = 3(0.1)/5 = 0.06 in/sec

If the velocity is Y-axis is off by 10%, what would be the new position ?

New velocity in y is 0.9 x 0 .06 = 0.054 in/sec

In 50 sec, the y- will move a distance [50(0.054)] = 2 .7 in.

Point-to-point Point-to-point and
straight line
Drilling and
boring

2-axis contouring with 3-aris contouring
switchable plane oontinuous path

2-axis contour
milling milling

Figure 6. Schematic illustration of drilling, boring, and milling with various paths.

Interpolator

The input speed of l in/sec in example 2 is converted into the velocity components by an
interpolator called the linear interpolator whose function is to provide the velocity signals to x
and y directions. Similarly we have circular and parabolic interpolators. See Figure 7.

i'f Quadrant ~ ---- Full
circle

Figure 7. Types of interpolation (a) linear, (b) continuous path approximated by
incremental straight lines, and (c) circular

Incremental and Absolute systems

CNC systems are further divided into incremental and absolute systems (Figure 8). In
incremental mode, the distance is measured from one point to the next. For example, if you
want to drill five holes at different locations, the x-position commands are x + 500, + 200, +
600, - 300, -700, -300 . An absolute system is one in which all the moving commands are
referred from a reference point (zero point or origin) . For the above case, the x-position
commands are x 500,700, 1300, 1000, 300, 0. (Figure 8) . Both systems are incorporated in
most CNC systems. For an inexperienced operator, it is wise to use incremental mode.

10

8

6

Figure 8. (a) Absolute versus incremental ; In absolute positioning, the move is specified
by x = 6, y = 8 ; in incremental, the move is specified by x=4, y=5 for the tool
to be moved from (2,3) to (6,8)

(b) Drilling 5-holes at different locations

The absolute system has two significant advantages over the incremental system :

Interruptions caused by, for example, tool breakage (or tool change, or checking
the parts), would not affect the position at the interruption.

If a tool is to be replaced at some stage, the operator manually moves the table, exchanges the
tool, and has to return the table to the beginning of the segment in which the interruption has
occurred . In the absolute mode, the tool is automatically returned to the position. In
incremental mode, it is almost impossible to bring it precisely to that location unless you
repeat the part program

2. Easy change of dimensional data

The incremental mode has two advantages over the absolute mode .

1. Inspection ofthe program is easier because the sum of position commands for each
axis must be zero . A nonzero sum indicates an error . Such an inspection is impossible
with the absolute system .

2. Mirror image programming (for example, symmetrical geometry of the parts) is simple
by changing the signs of the position commands.

Open Loop Control Systems

The open-loop control means that there is no feedback and uses stepping motors for driving
the leadscrew . A stepping motor is a device whose output shaft rotates through a fixed angle
in response to an input pulse (Figure 9) . The accuracy of the system depends on the motor's
ability to step through the exact number . The frequency of the stepping motor depends on the
load torque. The higher the load torque, lower would be the frequency . Excessive load torque
may occur in motors due to the cutting forces in machine tools . Hence this system is more
suitable for cases where the tool force does not exist (Example : laser cutting) .

Work table
Pulse
train a stepping
motor

Lead screw

Figure 9. Open loop control system

The stepping motor is driven by a series of electrical pulses generated by the MCU . Each
pulse causes the motor to rotate a fraction of one revolution. The fraction is expressed in
terms of the step angle, oc, given by

a = 360/N, degrees where N = number of pulses required for one revolution

If the motor receives "n" number of pulses then the total angle,

A = n (360/N), degrees

In terms of the number of revolutions, it would be (n/N)

If there is a 1 :1 gear ratio between the motor and the leadscrew, then the leadscrew has (n/N)
revolutions . If the pitch of leadscrew is p (in/rev), then the distance traveled axially, say x,

x = p(n/N)

can be used to achieve a specified x-increment in a point-to-point system.

10

The pulse frequency, f, in pulses/sec determines the travel speed of the tool or the workpiece .

60 f = N (RPM) where N = number of pulses per revolution,
RPM = RPM of the lead screw

The travel speed, V, is then given by V = p (RPM) where p pitch in in/rev

Example 3

A stepping motor has N = 150, p = 0.2"/rev ; If n = 2250 pulses, what is the distance
traveled in x-direction ? What should be the pulse frequency for a travel speed of 16
in./min ?

x = (0.2) (2250)/150 = 3"

16'= 0 .2 (RPM), from which, RPM = 80

f = (150) (80)/60 = 200 Hz

Example 4

A stepping motor of 200 steps per revolution is mounted on the leadscrew of a
drilling machine. If the pitch is 0.1 in/rev.,

a. What is the BLU ?
b. If the motor receives a pulse frequency of 2000 Hz, what is the speed of the
table ?

a. BLU = 0 .1/200 = 0.0005"

b. Table speed = (p) (RPM) = (0 .1) (60) (2000)/200 = 60 in/min

Closed-loop Control Systems

Closed -loop NC systems are appropriate when there is a force resisting the movement of the
tool/workpiece . Milling and turning are typical examples . In these systems (Figure 10) the DC
servomotors and feedback devices are used to ensure that the desired position is achieved .
The feedback sensor used is an optical encoder shown in Figure 11 . The encoder consists of
a light source, a photodetector, and a disk containing a series of slots. The encoder is
connected to the leadscrew . As the screw turns, the slots cause the light to be seen by the

photodetector as a series of flashs which are converted into an equivalent series of electrical
pulses which are then used to characterize the position and the speed. The equations remain
essentially the same as open-loop except that the angle between the slots in the disk is the
step angle, a.

Both the input to the control loop and the feedback signals are a sequence of pulses, each
pulse representing a BLU unit. The two sequences are correlated by a comparator and gives
a signal, by means of a digital-to-analog converter, (a signal representing the position error),
to operate the drive motor (DC servomotor) .

Work table
Input
do
Comparator DAC Gear
servomotor

Position
Feedback signal sensor

Figure 10. Closed loop control system

Signal pulses

Photocell Time
(a) (b)

Figure 11 . Optical Encoder (a) Device (b) Series of pulses emitted

12

Example 5

Consider a CNC worktable driven by a closed-loop control system consisting of a
servomotor, leadscrew, and optical encoder. The leadscrew has a pitch, p = 0.2" and
is coupled to the motor shaft with a screw to motor gear ratio of 1 :4. The encoder
generates 150 pulses per revolution of the leadscrew. If the number of pulses and the
pulse rate received by the control system are 2250 and 200 Hz respectively, calculate

a. Table speed
b. Motor speed in RPM
c. Distance traveled by the table

a. V= p(RPM) = 0 .2(RPM) = (0 .2) (60 f)/N = (0 .2) (60) (200)/150 = 16 in/min

b. RPM of the leadscrew = (60) (200)/(150) = 80
RPM of the motor = 320

c. x = p(n/N) = (0.2) (2250)/150 = 3"

Example 6

A do servomotor is coupled to a leadscrew which drives the table of a CNC machine
tool. A digital encoder, mounted at the end of the screw, emits 500 pulses per
revolution. If the pitch is 5 mm per rev, and the motor rotates 600 rpm (1 :1 gear
ratio), calculate the

a. Table speed
b. BLU
c. Frequency of pulses transmitted by the encoder

a. V= p(RPM) = 5 (600) = 3000 mm/min = 3 m/min

b. BLU = 5/500 = 0.01 mm

c. RPM = 600 = (60f)/N = 60 f/500 from which f = 5000 Hz

13

PRECISION IN CNC MACHINING

The combined characteristics of the machine tool and the control determine the precision of
positioning . Three critical measures of precision are :

o Resolution
o Accuracy
o Repeatability

Control resolution (BLU) is the distance separating two adjacent points in the axis movement
(the smallest change in the position) . The electromechanical components of the positioning
system that affect the resolution are the leadscrew pitch, the gear ratio, and the step angle in
the stepping motor (open loop) or the angle between the slots in the encoder (closed-loop).
The control resolution for a 1 :1 gear ratio of a stepped motor is,

Resolution = p/N where p = pitch, and N = 360/a

Features smaller than the control resolution could not be produced . The programming
resolution can not exceed the control resolution .

Accuracy of a CNC system depends on the resolution, the computer control algorithms, and
the machine inaccuracies . The inaccuracy due to the resolution is considered to be (1/2)BLU
on the average. The control algorithm inaccuracy is due to the rounding off the errors in the
computer which is insignificant. The machine inaccuracy could be due to several reasons
(described below) . The designer minimizes this inaccuracy to be under (1/2)BLU and hence

Accuracy = (1/2) Resolution + Machining inaccuracy = BLU

Repeatability is a statistical term associated with accuracy . It refers to the capability of a
positioning system to return to a programmed point, and is measured in terms of the errors
associated with the programmed point. The deviation from the control point (error) usually
follows a normal distribution in which case the repeatability may be given as +/- 3a where a
is the standard deviation. The repeatability is always better than the accuracy . The mechanical
inaccuracy can be considered as the repeatability . Figure 12 shows the difference between the
accuracy and the repeatability .

Machining Inaccuracy

Cutting tool deflection, machine tool chatter, mechanical linkage between the leadscrew and
the tool, and thermal deformations are the chief contributing factors . The leadscrew transmits
the power to the table or toolholder by means of a nut that engages the leadscrew . This will
create what is known as "backlash"due to the friction between the screw and the nut. If the
nut consists of ball bearings, the friction is reduced . Thermal deformations are significant.
For example, a temperature difference of 1 °C along 1000 mm can cause an error of 0.01 mm.

14

EMEMOMME
MOMEMENN
MMMMMMMM
MEME ME"O
MEN"E"""
MMOMMOME
s
ONNEEMEN
EMOMMEN
IMMEMENE
MENNOMME EMMMOMME M"MM IMSN
ME MEN .... .... ...LO...
MI No MEMM EME" MMMMMMMM
MMEMEMEN MOMMOMME M"""M"N
MEMEMMEN """" MM""
Low Accuracy Low Accuracy High Accuracy
Low Repeatability High Repeatability High Repeatability

Figure 12. Diagram showing the difference between accuracy and repeatability

Example 7

What is the control resolution for a 4 :1 gear ratio (motor: leadscrew), pitch of
leadscrew 0.2 in/rev, and the motor receives 600 pulses per revolution

Since the motor shaft rotates 4 times faster than the leadscrew, N = 600/4 = 150
Resolution = 0.2/150 = 0.001333"

What would be the accuracy and repeatability if the machining inaccuracy is about
(1/2)BLU ?

Accuracy = 0.001333/2 + 0 .001333/2= 0.001333"

Repeatability = +/- 0.00067"

15

PART PROGRAMMING FOR CNC

The transfer of an engineering blueprint of a product to a part program can be performed
manually using a calculator or with the assistance of a computer language . A part programmer
must have an extensive knowledge of the machining processes and the capabilities of the
machine tools . In this section, we describe how the part programmers execute manually the
part programs.

First, the machining parameters are determined . Second, the optimal sequence of operations
is evaluated . Third, the tool path is calculated . Fourth, a program is written. Each line of the
program, referred to as a block, contains the required data for transfer from one point to the
next.

A typical line for a program is given below .

N100 G91 X -5.0 Y7 .0 F100 S200 T01 M03 (EOB)

The significance of each term is explained below .

Sequence Number, N

Consisting of typically three digits, its purpose is to identify the specific machining operation
through the block number particularly when testing a part program.

Preparatory Function, G

It prepares the MCU circuits to perform a specific operation . The G-codes (some) are shown
in Table 1 . G91 implies incremental mode of operation.

Dimension Words

1. Distance dimension words, X,Y,Z

2. Circular dimension words, I,J,K for distances to the arc center

3. Angular dimensions, A,B.C

While (1) and (3) are expressed either by incremental or absolute mode, (2) is always in given
in incremental mode. All angular dimensions are specified in revolutions or degrees.

In the above block, X moves a distance of 5 in. in the negative direction while Y moves a
distance of 7 in. in the positive direction. Other axes remain stationary. In some systems,
actual distances are used. In others, the dimension words are programmed in BLUs .

16

Feedrate, F

It is expressed in in/min or mm/min and, is used in contouring or point-to-point or straight-cut
systems . For example, a feedrate of F100 implies 100 in/min or 100 mm/min . Feedrates are
independent of spindle speed.

In linear motions, the feedrate of the cutting tool is not corrected for the cutter radius . But
in circular motions, the feedrate should be corrected for the tool radius as follows :

F = [(part contour radius ± tool radius)/part contour radius] (required feedrate)

For cutting around the outside of a circle, the plus sign in the above equation is used, and the
feedrate is increased. For cutting around the inside of a circle, the minus sign is used, and the
feedrate is decreased .

Example 8

See Figure 5(a). If the required feedrate is 6 in/min, part contour radius is 1 .5 in,
and the cutter diameter is 1 in, what is the feedrate athe top and bottom circles ?

Feedrate at the top is to be 8 in/min and at the bottom is to be 4 in/min.

Spindle speed, S

Programmed in rev/min, it is expressed as RPM or by a three-digit code number that is
related to the RPM.

Toolword, T

Consisting of a maximum of five digits, each cutting tool has a different code number. The
tool is automatically selected by the automatic tool changer when the code number is
programmed in a block.

Miscellaneous Function, M

Consisting of two digits, this word relates to the movement of the machine in terms of spindle
on/off, coolant on/off etc shown in Table 2.

EOB

The EOB character is used at the end of each block to complete a line.

17

Table . .1 Preparatory commands (G-code)
G00 Point-to-point positioning
G01 Linear interpolation
G02 Clockwise circular interpolation
G03 Counter-clockwise circular interpolation
G04 Dwell
G05 Hold
G33 Thread cutting, constant lead
G40 Cancel tool nose radius compensation
G41 Tool nose radius compensation - left
G42 Tool nose radius compensation - right
G43 Cutter length compensation
G44 Cancel cutter length compensation
G70 Dimensions in inches
G71 Metric dimensions
G90 Absolute dimensions
G91 Incremental dimensions
G92 Datum offset

Table . .2 Miscellaneous commands (M-code)
M00 Program stop
M01 Optional stop
M02 End of program
M03 Spindle start clockwise
M04 Spindle start counter-clockwise
M05 Spindle stop
M06 Tool change
M07 Mist coolant on
M08 Flood coolant on
M09 Coolant off
M10 Clamp
Mll Unclamp
M13 Spindle clockwise, coolant on
M14 Spindle counter-clockwise, coolant on
M30 End of tape, rewind

Tables 1 and 2 : G and M codes used in CNC systems

18

4-7-2 G Functions (SEICOS-MII)

G code Group Function
GOO Positioning (rapid traverse)
GO1 Linear interpolation (cutting feed) .
01
G02 Circular interpolation CW
G03 Circular interpolation CCW
G04 Dwell

G07 00 SIN interpolation (designation of virtual axis)
G09 Exact stop check
G10 Offset amount and work zero point offset amount setting
G17 Designation of X-Y plane
G18 02 Designation of Z-X plane
G19 Designation of Y-Z plane
G20 06 Inch input
G21 Metric input;
G22 Stored stroke, limi t,ON
04~
G23 Stored'--s troke"- limit OFF
G27 Return to reference paint
G28 Return to reference-pant:_-_. ..
G29 00 Return from reference point `'
G30 Return to 2nd reference point 4
G31 Skip function

G40 07 Tool diameter compensation cancel
G41 Tool diameter compensation to left
G42 Tool diameter compensation to right
G43 Tool length compensation
G44 08 Tool length compensation
G49 Tool length compensation cancel
G45 Tool offset expansion
G46 00 Tool offset reduction
G47 Tool offset double expansion
G48 Tool offset double reduction

G50 11 Scaling cancel
G51 Scaling

G codes with " " are set when the power is .turned on .
G40, G49 and G80 are set by resetting the NC unit .

G code Group Function
G52 00 .Local coordinate system setting
G53 Machine coordinate system selection
G54 Work coordinate system 1 selection
G55 12 Work coordinate system 2 selection
G59 Work coordinate system .6 selection
G60 00 I One directional positioning
G61 Exact stop check mode
G63 13 I Tapping mode
G64 Continuous cutting mode
G65 00 Macro call
G66 14 Macro modal call A
G67~ C Macro modal call cancel

G73 + Pec k dri l ling cycle
G74 Reverse tapping cycle
G76 I Fine boring
G80 ` Canned cycle cancel
G81' Dr illing cycle, sp ot boring
G82 Drilling cycle, counter boring
G83 09 Peck drilling cycle
G84 ( Tapping cycle
G85 Boring cycle
G86 I Boring cyc le
r
G87 Back boring cycle -'"
G88 Boring cycle
G89 I Boring cycle
G90 03 L Absolute programming
G91 Incremental programming
G92 00 Programming of absolute zero point

G98 10 I Initial level return (canned cycle)
G99 R point level return (canned cycle)
G501 15 Programmable mirror image cancel
G511 Programmable mirror image

4 - 30

4-7-3 M Functions
(* : Optional function)

M I Function name M Function name
Idle cutting time reduction
00 Program stop *33
(modal)
(Idle cutting time reduction
01 Optional stop *34
(unmodal)
02 End of program *35 Automatic start ON

03 (Spindle forward *36 Automatic start OFF
04 Spindle reverse *37
Spindle no-load detect function
05 (Spindle stop *38
stop

06 Tool change ATC *39 M38 cancel

*07 Mist coolant start *40 Tool nose air blow ON

08 Flood coolant start *41 Tool nose air blow OFF

09 (Mist coolant stop *42
*10 Mist coolant attitude 1 *43

*11 Mist coolant attitude 2 *44

*12 Work count *45 Spare tool offset enabled

13 Spindle forward & coolant start ''*46 (Spare tool offset disabled
14 Spindle reverse & coolant start *47 Jet coolant start

15 M13/M14 stop 48 (Feed rate override enabled

*16i Measurement air blow ON 49 Feed rate override 100%
*17 Measurement air blow OFF *50 Oil hole coolant start
*18~ Measuring spindle orientation *51
19 Spindle orientation *52 Tool breakage detect
*20~ Machining time monitoring *53
*21 *54
*22 *55
*23 *56
*24 *57
*25 *58
*26 Melodia (1) *59
*27 Melodia (2) *60 Work change APC
*28 Setting load level 0 *61
*29 Setting load level 1 *62
30 End of tape *63

*31 Chip conveyor start *641
*32 M33 cancel *65

M Function name M Function name

*66
*67
*68 Additional axis clamp
*69 Additional axis unclimp
*70 M70 output
*71 M71 output
*72 M72 output
*73 M73 output
*74 Skip selection OFF
*75 Skip selection ON
*76 .
*77
*78 Additional axis clamp
*79 Additional axis unclamp
*80 Tool nose air blow ON
*81
*82
i
*83
*84
*85
Measurement NG tool breakage
*86
detect
*87

*90
*91
*92
*93
*94
*95
*96
*97
98 Subprogram call

99 End of subprogram

4- 3 2

M Maintenance mode
*1001 Arm swing-in to spindle side
*101
*102. Arm advance
*103 Arm turn CW
*104 Arm turn CCW
*105 Arm retract
*106 Arm slide to home position__
*107
*108 Arm slide to magazine side
*109
*110
*111
*112
*113
*114
*115
*116
*117
*118
*119 Orientation
*120 Magazine positioning pin OUT
*121 Magazine positioning pin IN 1
*122
*123,
*124 Pallet slider advance (APC)
*125 Pallet unclamp (APC)
*1261 Pallet slider retract (APC)
*1271 Pallet right turn (APC)
*128 Pallet left turn (APC) -
1
*129 Pallet unclamp (APC)

4-33

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