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How to improve part quality from your
CNC machining center with ease
-----A new technology
Charles Wang
Optodyne, Inc
1180 Mahalo Place
Rancho Dominguez, California 90220
WWW.optodyne.com
Outline
• Introduction
• What are the 3D volumetric positioning
errors?
• How to measure the 3D volumetric
positioning errors?
• What is the vector technique or sequential
step diagonal measurement?
• How to compensate 3D volumetric
positioning errors.
• Experimental verification
• Summary and conclusion
1
Why measure and compensate 3D volumetric
positioning errors?
• Worldwide competition and quality standards
ISO 9000 and QS 9000.
• Tighter tolerance on machines and parts.
• Twenty years ago,
Linear errors, lead screw pitch and thermal
expansion are the major errors.
• Now,
squareness and straightness are the
major errors.
• To achieve higher positioning accuracy,
the measurement and compensation
of squareness and straightness errors are
very important.
Linear Errors
x(x)
A
B
x
C
For x-axis motion
A: Starting position
B: Programmed position
C: Actual position
BC: Linear Error
BC = x(x)
x(x): error in x-direction as function of x
( Lead screw pitch error)
Similarly for y-axis and z-axis motion
y(y): error in y-direction as function of y
z(z): error in z-direction as function of z
Volumetric Errors
z
C
y
z(x)
A
B
y(x)
x(x)
x
For x-axis motion
A:Starting position
B:Programmed position
C:Actual position
BC: Volumetric error
BC = x(x) ex + y(x) ey + z(x) ez
x(x): error in x-direction as function of x
y(x): error in y-direction as function of x (horizontal straightness)
z(x): error in z-direction as function of x (vertical straightness)
Similarly for y-axis and z-axis motion
x(y): error in x-direction as function of y
y(y): error in y-direction as function of y
z(y): error in z-direction as function of y
x(z): error in x-direction as function of z
y(z): error in y-direction as function of z
z(z): error in z-direction as function of z
2
The 21 rigid body errors
For a 3-axis machine, there are 21 rigid body errors
• 3 Linear displacement errors:
Dx(x), Dy(y), and Dz(z)
• 3 Vertical straightness errors:
Dy(x), Dx(y), and Dx(z)
• 3 Horizontal straightness errors:
Dz(x), Dz(y), and Dy(z)
• 3 Roll angular errors:
Ax(x), Ay(y), and Az(z)
• 3 Pitch angular errors:
Ay(x), Ax(y), and Ax(z)
• 3 Yaw angular errors:
Az(x), Az(y), and Ay(z)
• 3 Squareness errors: Øxy, Øyz, Øzx,
6 errors per axis
3 squareness errors
3
What are 3D volumetric positioning errors?
The volumetric positioning errors are:
3 displacement errors Dx(X), Dy(Y), and Dz(Z)
6 straightness errors Dy(X), Dx(Y), Dx(Z)
Dz(X), Dz(Y), Dy(Z)
3 squareness errors Φxy, Φyz, Φzx
A total of 12 errors.
Total errors in each direction are:
Dx(x,y,z) = Dx(x) + Dx(y) + Dx(z)
Dy(x,y,z) = Dy(x) + Dy(y) + Dy(z) + Øxy*x/X
Dz(x,y,z) = Dz(x) + Dz(y) + Dz(z) + Øyz*y/Y + Øzx*x/X
The vector sum of positioning errors
• The error in each axis direction is the sum of errors caused by
all 3 axes movement plus the errors caused by the non
-perpendicular of the 3 axes.
• The positioning error in an arbitrary point within the working
volume is composed by the positioning errors of the
individual axes in all 3 axis directions.
• The total error at each point is the vector sum of
errors in all 3 axis directions.
How to measure the 3D volumetric
positioning errors?
Conventional laser interferometer
very complex and expensive optics (Wollaston Prism)
difficult to setup and align and
very time consuming
Laser vector technique*
simple and efficient
easy setup, alignment and operation
saves time, measurement in hours instead of days
* A vector measurement method and apparatus. US Patent 6,519,043,
February 11, 2003.
4
Spindle
Wallaston Prism
Straightness
Reflector
Optical Square
Laser
Straightness & Squareness Measurement Using a Wollaston Prism and
Optical Square
Measurement of the diagonal displacement
accuracy ASME B5 and ISO 230-6
Body diagonal displacement errors before the compensation.
The total error is 90 micron.
5
ASME B5.54 or ISO 230-6 body
diagonal displacement error
measurement
• The volumetric positioning errors, including 3
displacement errors, 6 straightness errors and 3
squareness errors, will show as the 4 body
diagonal displacement errors.
• It is a good measure of volumetric accuracy. But
do not have enough data to determine the
displacement error, vertical straightness error
and horizontal straightness error of each axis.
What is the vector technique?
Laser vector technique developed by Optodyne
US Patent # 6,519,043, 2/11/2003
Measures the volumetric positioning errors,
3 displacement errors
6 straightness errors and
3 squareness errors,
in 4 body diagonal sequential steps displacement
measurement.
Measurement can be performed in a few hours
instead of a few days.
Laser Vector (or Sequential step diagonal)
Measurement Technique
• Sequential Step Body Diagonal
Displacement errors
• Separate X-axis, Y-axis and Z-axis
movement.
• 3 times more data, or 12 sets of data.
• All variables are separated.
• Solve the 3 displacement errors, 6
straightness errors and 3 squareness
errors.
6
Laser vector method
Sequential diagonal path
Results:
- straightness errors
Dy(x), Dz(x), Dx(y), Dz(y), Dx(z), Dy(z)
- squareness errors
Bxy, Bzx, Byz
- diagonal displacement test
Ed
Major advantages of single aperture
optical arrangement
• Reduced size of optical components.
Hence the laser system is smaller and
more compact.
• Able to use a flat-mirror as target for large
lateral movement. Hence the laser vector
and laser ballbar measurement are
possible.
7
Volumetric compensation
• Compensate 3D volumetric positioning errors by
high-end CNC controllers, such as Fanuc 15, 16/18,
30i/31i/32i, Siemens 840D/810D, Heidenhain 450,
Fagor, Fidia, etc.
• Compensate 3D volumetric positioning errors by
modifying the part program for CNC machines with
low-end controllers.
The measurement volume only has to be larger than
the part volume, which usually is less than 20% of
the working volume. This further reduces the
measurement time.
Experimental Verifications
X-axis errors
•
•
•
•
•
•
•
•
•
•
•
•
Target
0.0
25.0
50.0
75.0
100.0
775.0
800.0
825.0
850.0
875.0
900.0
DXX
0.0000147
-0.0010466
-0.0021427
-0.0028001
-0.0041913
-0.0218803
-0.0215804
-0.0219705
-0.0216299
-0.0210416
-0.0207334
DXY
DXZ
0.0
0.0
0.0003849 -0.0011529
0.0014003 -0.0023086
0.0020966 -0.0029604
0.0030704 -0.0032527
0.0041541 0.0027603
0.0037406 0.0028455
0.0034518 0.0035008
0.003313
0.0038701
0.0028759 0.0036788
0.0026314 0.0034715
8
Y-axis errors
• Target
DYY
•
•
•
•
•
•
•
•
•
•
•
•
•
0.0000118
-0.0032729
-0.0048146
-0.0060457
-0.0066843
-0.006398
-0.0171938
-0.0159006
-0.015133
-0.0135387
-0.0133751
-0.0136334
-0.0144286
0.0
20.0
40.0
60.0
80.0
100.0
600.0
620.0
640.0
660.0
680.0
700.0
720.0
DYX
0.0000352
-0.0008479
-0.0014667
-0.0018009
-0.0022469
-0.0023742
-0.0038179
-0.0033269
-0.0033682
-0.0028901
-0.0027834
-0.002417
-0.0019177
DYZ
0.0
-0.0007612
-0.0015055
-0.0024554
-0.0026467
-0.0032861
0.0050573
0.0056786
0.0065169
0.0073864
0.0075783
0.0082402
0.0085888
Z-axis errors
• Target
DZZ
DZX
•
•
•
•
•
•
•
•
•
•
•
•
•
0.0000118
-0.010674
-0.018841
-0.0195394
-0.0194431
-0.0193279
-0.0158113
-0.0154574
-0.0158641
-0.015632
-0.0156527
-0.0154328
-0.0160066
-0.0001535 -0.000179
-0.0005031 -0.000539
0.0007003 -0.0020058
0.0013789 -0.0037519
0.0019572 -0.0052592
0.0025898 -0.006708
0.0214316 -0.0265376
0.021957
-0.0272654
0.0221578 -0.0279952
0.0229769 -0.0290042
0.0232969 -0.0304087
0.0237272 -0.0317971
0.0246671 -0.0327949
0.0
20.0
40.0
60.0
80.0
100.0
600.0
620.0
640.0
660.0
680.0
700.0
720.0
DZY
Part program without compensation (left) and with
compensation (right)
9
Parts machined without compensation
(left) and with compensation (right)
Measured parts accuracy with and without
compensation
• The errors in X and Y directions are relatively small.
This is because the machine was compensated for lead
screw pitch errors.
• Without compensation, the squareness error is rather
large. Errors in + 45 degrees and -45 degrees are
differed by 0.0015” (0.038 mm), which corresponds to a
squareness errors of 70.5 arcsec.
• With compensation, errors in +45 degrees and – 45
degrees are differed by 0.0003” which corresponds to a
squareness error of 14.1 arcsec, a significant
improvement.
Summary and conclusion
The advantages of compensate part program are:
• Improves the parts accuracy for any CNC machining
centers without high-end controllers.
• No need to measure over the whole machine working
volume. Only over the part volume is measured. It
saves measurement time, more accurate, and more
compensation points.
• Works in a real shop environment, such as in summer or
winter. The measured positioning errors include the
effect of material thermal expansions and distortions,
and also the angular errors.
• It is a more viable or economic approach to improve
parts accuracy.
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