Procedia Manufacturing
Volume XXX, 2015, Pages 1–22
43rd Proceedings of the North American Manufacturing Research
Institution of SME http://www.sme.org/namrc
CNC Machine Tool Work Offset Error Compensation
Method
Jie Gu, John S. Agapiou and Sheri Kurgin
General Motors R&D
Jie.1.gu@gm.com, John.agapiou@gm.com, sheri.kurgin@gm.com
Abstract
Machine tool accuracy and repeatability is one of the most important considerations for manufacturing
parts with the required quality for consistent performance in their assemblies. One of the most
challenging areas has been the ability to quickly identify and evaluate the quasi-static and dynamic
machine errors and apply the corresponding error models to compensate. Because there are many
challenges associated with some methods, including the cost in design, analysis and control of
precision machine tools, the compensation method has been the most effective approach to control part
quality. However, error compensation by measurement of geometric errors is greatly affected by the
error modeling and error measurement methods, which could require significant machine downtime to
implement. This paper presents the development of a Global offset compensation method utilizing the
measurements of the machined part(s). The Global Offset for a machine tool is estimated through a
model while utilizing the computed deviation between the measured and nominal dimensions of the
part. Furthermore, the paper presents several other compensation concepts supporting the Global offset
method. The strengths and limitations of all compensation methods are also discussed.
Keywords: Error Compensation, Machine Accuracy, Machined Part Quality
1 Introduction
CNC (Computerized Numerical Controlled) Machines are being used increasingly for high to
medium volume manufacturing (Stephenson, D., Agapiou, J.). CNC machines allow manufacturers to
adjust for changing product designs and volume requirements, and are extremely accurate. The goal of
a CNC machine is to produce a high quality part by achieving the dimensional tolerance of the CAD
model. Precision machining is key to the die and mold industry, automotive powertrain components
(i.e. engines, transmissions, etc.), and large components in the aerospace and defense industry. Errors
due to machining will impact not only the assembly of the machined parts, but also introduces larger
product performance variability. Therefore, the accuracy and repeatability of machine tools are often
Selection and peer-review under responsibility of the Scientific Programme Committee of NAMRI/SME
c The Authors. Published by Elsevier B.V.
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the limiting factor for achieving and maintaining part quality because the positional error of a machine
axis is affected by several factors attributed to the machine tool itself, fixture and cutting process. The
machine tool errors are either quasi-static or dynamic. The quasi-static error sources are the
geometric/kinematic errors of the machine axes and moving loads, while the dynamic errors are
dynamic loads, self-induced and forced vibrations, thermo-mechanical (thermal deformations of the
machine structure and the workpiece, which are due to both internal and external heat sources), cast
part-to-part variation, and motion and software control errors of the system (Schwenke, Knapp,
Haitjema, Weckenmann, & Schmiitt, 2008) (Ramesh, Mannan, & Poo, 2000a). Even though the
geometric errors may be compensated, the dynamic errors cannot be fully eliminated at the design
stage, and therefore real time compensation is required (Fraser, Attia, & Osman, 2004) (Mayr, et al.,
2012) (Ramesh, Mannan, & Poo, 2000b). The errors due to the process such as tool wear and
deflection, workpiece deflection, workpiece location and clamping errors are not generally considered,
although they affect part quality. The initial approach to machine dimensional stability has been to
first provide machine calibration as necessary, and secondly to maintain a stable shop environment to
reduce the thermal effects. The second objective has been very challenging in a large manufacturing
plant and often cost prohibitive in full scale production. The first objective requires: (1) mathematical
or empirical models to represent the quasi-static errors of machine tools, (2) method(s) to accurately
predict the errors and/or the parameters in the models that are essential for developing a compensation,
and (3) compensation scheme that can be performed quickly to improve machine tool accuracy and to
minimize production downtime.
The aim of this paper is to summarize the common types of work offset methods and introduce an
innovative compensation method called Global Offset. This new automated compensation method for
machine tools is low investment and it is based on the dimensional measurements of identical part(s)
in a CMM (Coordinate Measurement Machine); it estimates the offsets in the WCS (Work Coordinate
System) to compensate the machine tool errors including the fixture and table/pallet errors together
with some of the dynamic errors due to part clamping, tool deflections, and average temperature
changes in the workspace.
2 Literature Review
During the early days of CNC machine tools, quasi-static errors accounted for about 70% of the
total error; today’s compensation approaches have reduced most of the geometric errors. However,
dynamic errors are still prevalent since they cannot be compensated completely and therefore are
considered the most significant errors. Our experience with large and medium size machine tools
during the last 15 years indicates that the error budget is distributed as follows among the sources of
error: 40-50% on static/geometric, 30-40% on dynamic (thermal, part and tool deflection, etc.), 1020% on environment, and 5-10% on measurement. It is also determined that 65-70% of the static error
is due to axes positioning and squareness errors especially for larger size machine tools. Machine tools
are sensitive to a variety of random influences, such as a crash, varying thermal state, possible
contamination, wear of moving elements, etc. which may result either in progressive errors (such as
drift which progressively degrade their accuracy over time) or in dramatic, permanent changes in
performance. If this occurs, the once-a-year or every few years calibration procedure is not capable of
catching these adverse changes in machine tool performance when they occur, resulting in batches of
parts being machined by an out-of-specification machine tool. In order to avoid this problem, various
methods have been developed as will be discussed next.
In the last two decades, several international standards for machine tool accuracy evaluation have
been developed (ISO-230-2, 2006) (ISO-230-6, 2002) (ASME-B5.54, 2005). Most of the machine tool
manufacturers incorporate such standard measurements for acceptance testing to prove out machines,
while users consider them as machine diagnostic solution (targeted to remove variation from the
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machining process). In addition, over the last three decades, error models have been developed based
on kinematic analysis of the machine tool axes to quantify the quasi-static errors in the work space as a
function of the individual machine tool geometric errors using rigid body kinematics as explained in
Refs. (Reshetov & Portman, 1988), (Weck, 1984) and many others found in the reference of papers
(Schwenke, Knapp, Haitjema, Weckenmann, & Schmiitt, 2008) and (Ramesh, Mannan, & Poo, 2000a)
for machine compensation. The second approach is the indirect measurement of the machine errors
superimposed at specified X,Y,Z positions mapped in the machine tool workspace; it requires the
simultaneous movement of two or more axes at specified intervals or a grid. The error is identified as
the difference among the actual and measured values of the displacement at the specified locations.
Such indirect measurements are made using artifacts, contour or circular paths, or multilateration (i.e.
using the diagonals of the workspace). Large numbers of machine tool manufacturers provide an error
mapping and a subsequent compensation of geometric errors in the same manner as has been well
established in CMMs (Coordinate Measuring Machines). However, machine tool accuracy could
change after the machine installation in the production floor and changes may occur slowly during
operation as a result of wear on moving parts, thermal changes and load effects, hysteresis effects, or
even minor accidents. Therefore, recalibration of the machine is very important to compensate for
geometrical errors such as positioning, straightness, squareness and rotation. However, due to the
difficulty of direct measurement of the relative thermal displacement δ(x,y,z,t) between the tool and
the workpiece during machining, control systems based on inductive and deductive approaches are
used. In the inductive approach, the components of the vector δ(x,y,z,t) are empirically related to
temperature, which is easily measured at some strategic points on the structure. During operation, the
measured temperatures are used to estimate the position error δ(x,y,z,t) and to activate the control
system (Weck, Schuze, Michels, & Bonse, 1994) (Chen, Yuan, Ni, & Wu, 1993). Since the empirical
based functions bear no physical similarity to the actual phenomena, the solution is unreliable outside
of the range of tested inputs. In addition, the information contained in the discrete temperature
measurements is incomplete and therefore the problem is not uniquely defined.
To overcome these problems, an alternative deductive approach was developed using numerical
models to fully describe the thermal and deformation processes which take place in the structure (Sata,
Takeuchi, Sakamoto, & Weck, 1981) (Moriwaki, 1988). Thermal loop analysis was proposed to
describe the thermal behavior of an entire machine tool using a path across the assembly of its
mechanical components (Zhu J. , 2008); thermal error models (based on thermal modal analysis) are
used to define the thermal links along the thermal loop. These approaches also suffers from a number
of drawbacks because: (1) the magnitudes of the heat sources are determined from off-line calibrations
that result in poor predictions, (2) the numerical models are either inaccurate or too slow to be used in
real-time control applications, and (3) the nonlinear thermoelastic behavior of the structural joint is
neglected.
A generalized modeling was proposed (Fraser, Attia, & Osman, 2004) to eliminate the limitations
of the inductive and deductive methods, by incorporating an inverse heat conduction solver to estimate
the heat input to the structure in real-time. The approach also provides the frame work for developing
a generic, multi-variable control system, which is capable of dealing with nonlinear structures. This
method requires: (1) modeling and monitoring the temperature and thermal distortion of the machining
system, including the part; (2) characterization of the transient thermal field and the thermal
deformation pattern in a typical part; (3) identification of the thermal boundary conditions and heat
input to the machining system in order to compensate the thermal deformation of the machine tool
structure. However, this method is not yet either fully implemented or validated. Finally, machine tool
accuracy compensation approaches due to thermal and machining process errors have been lagging.
Variation propagation modeling has been proven to be an effective way for variation reduction and
design synthesis in multi-operational manufacturing processes. However, previously developed
approaches for machining processes did not directly model the process physics regarding how fixture,
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datum, and machine tool errors generate the same pattern on part features. Consequently, it is difficult
to distinguish error sources at each operation.
Furthermore, many methods for enhancing the accuracy of CNC machine tools have been
proposed over the years (Wang, Yu, & Liao, 2006) (Rahou, Cheikh, & Sebaa, 2009) (Yeung, 2004).
An integrated geometric error modeling, identification and compensation method for machine tools
was developed based on the individual axes errors (Zhu, et al., 2012) (Fletcher, Postlethwaite, & Ford,
2001). It identifies the 21 translational geometric error parameters associated with linear-motion axes
based on a laser interferometer, and 6 angular geometric error parameters for each rotation axis based
on a ball-bar. An identification method is used based on the model to recognize these geometric errors
that are compensated by correcting corresponding NC codes. The results showed that the integrated
method was effective and applicable in multi-axis machine tools. More recently, laser calibration data
analysis software is being provided by a few vendors that brings new levels of functionality and
flexibility to compensation methods by utilizing laser interferometer calibration systems combined
with rotary axis calibrators to evaluate rotary axis positioning performance (with ± 1 arc sec accuracy)
in addition to the linear axis measurement. The use of a laser interferometer has been the most
common method to fully assess geometric errors. Unfortunately, this technique has disadvantages
because it requires several days (resulting in significant downtime and cost) and the usage of a
volumetric error synthesis model.
Volumetric compensation has been achieved by creating an error map of the workspace volume in
the machine using a specified compensation scheme and the proper laser equipment to acquire the
required measurements. The implementation details depend on the type of CNC machine and its
controller and on the software used to implement it. There are several systems on the market and each
one utilizes its own software (Flynn, 2011) (Wang C. ) (Shen, Yang, & Wang, 2008). The Telescoping
Magnetic Ball-Bar test is an easy and quick method to diagnose machine tool performance and
especially dynamic errors (ASME-B5.54, 2005) (Ziegert & Mize, 1994). Furthermore, telescoping
ball-bars are very practical, convenient and are a comprehensive tool for assessing the contouring
accuracy of machine tools. Often a laser tracer is used that follows the target reflector positioned on
the spindle in a spatial grid (error map) and records the spatial displacement (Schwenke, Franke, &
Hannaford, 2005) (Umetsu, Furutnati, Osawa, Takatsuji, & Kurosawa, 2005). Conventional laser
trackers reduce the machine calibration to less than a day depending on the workspace and the density
of the grid. The manual process is still time consuming, error prone, and tedious. However, triggering
techniques are becoming available with active targeting to reduce the measurement time and improve
accuracy. These systems do have concerns with respect to compensation metrology revolving around
targeting, triggering, and accuracy (Flynn, 2011).
While the compensation methods described above have merit, they are not commonly used in
industry today at regular intervals. The measurement of the individual errors with laser interferometer
is time consuming (several days) and requires highly skilled personnel to run, which makes the
method too expensive to be utilized periodically in a manufacturing system that includes several or
dozens of CNC machining centers. The volumetric compensation is more effective but not yet fully
adapted for production.
Therefore, gaging touch probe has been used for contact scanning of post-process parts fixed in
machining centers. It has the capability to perform both surface scanning and touch functions for
workpiece positioning and measurement. The probe measures the finished part feature(s) location or
verifies that the part face is correctly oriented. The difference among the actual and nominal values
can be compensated by either correcting the individual feature location or using the conventional
offset method and adjusting the location of individual part faces, as will be discussed in a following
section. The conventional offset method requires a special spreadsheet to evaluate the average offset
of the features at each face or part rotation. In addition, the inspection time of all or only critical
features in the part could be as long as or longer than the machining cycle itself; in addition, more
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time is required to thoroughly wash all machining chips from the part to ensure accurate
measurements.
Another approach that could account for geometric errors has been the measurement of a master
part or Spatial Reference System (Mou & Liu, 1992) (Agapiou & Du, 2007) (Omari, Ajao,
Kampmann, & Schmadel, 2007) with known dimensions. There are several specific test artifacts that
can be measured using the machine tool touch probe and the performance of the machine in measuring
these test artifacts can be used as an interim measure of capability as recommended for CMMs. The
speed of this method depends mainly on the complexity of the artifact, which affects the number of
points required for the measurements (Agapiou & Du, 2007). The artifact methods require: (1) setup
of artifact on the pallet, (2) probing the artifact at specified position(s) to collect data for the controlled
features, and (3) running the data analysis to determine machine performance. Depending on the
artifact design characteristics, this method can be used to evaluate the machine’s positioning and
squareness errors (i.e. using a calibrated tetrahedron (Omari, Ajao, Kampmann, & Schmadel, 2007) or
ball-bar); the difference between the measured dimensions and reference dimensions is used to model
the machine tool error with kinematics. The results are used to remove inspection error from the
machine tool. When artifacts (calibrated tetrahedron, ball-bar, identical production well-calibrated
part, step gage, etc.) are used to evaluate machine performance, the procedure requires using the
artifact immediately after a machine calibration to obtain the baseline performance of the machine.
The artifact method will not identify all dynamic machining errors because the spindle load and part
distortion due to cutting forces, clamping pressures, error due to part locating surfaces, and/or thermal
errors induced by the machining process aren’t present during gaging. In addition, the probing errors
must be very small (at least a magnitude smaller than the machine measured errors) for the
measurements to be accurate. If 3D probing is required, the touch probe must have a compensation
map for the stylus sphere. The artifact must be also very stable and highly accurate. Because of the
above drawbacks, this method is not highly utilized in high to medium volume production.
A logical next approach is to measure the finished part in a CMM to determine the compensation
parameters for the machine tool and overcome some of the limitations of either measuring the part or
artifact on the machine. The most common method of compensating a CNC machine is to make small
adjustments to the work offsets of the machine. Work Offset (also known as Work Coordinate System
or Fixture Offset) is a method of positioning the cutting tool based on the machine zero position. Work
offset may be adjusted from its nominal values to compensate the position of its associated machined
features, while allowing the tool path to be programmed to the nominal part print position of the
feature. The work offset method relaxes the monitoring ranges for quasi-static errors and some
dynamic errors and the need for periodic calibration. Rather, it requires only simple CNC
programming and CMM production measurement data of the machined parts. Therefore, the work
offset technique provides the ability to quickly and appreciably reduce the impact of machining errors
on part quality.
3 Error Compensation Concept
Consider a 4-axis CNC machine with a B-rotary table whose spindle and table motion are
programmed in a coordinate system as illustrated in Fig. 1. There are two aspects in the concept of
cutting tool location control: (1) control the tool to a nominal location, and (2) control the tool to an
accurate location.
Case 1 “Control the tool to a nominal location” is intuitive. If one wishes to drill a hole in a part at
(x,y) location with L depth, one can command the tool to move to point (x,y,z1) and then (x,y,z2 ) in
the coordinate system, where L=z2-z1. A hole programmed to the nominal position may not be
machined accurately enough to meet the part print specification (with respect to location and
orientation) due to possible machine axes errors (while the calibration is outdated), table center
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location error, coordinate origin location error, and part/fixture alignment errors. It is a challenge to
make an accurate hole in an error-prone environment, especially when the errors are numerous, and
their nature may not be well understood.
In this case, there are various strategies to reduce machine tool errors that adversely affect part
quality. These are: (a) build an accurate machine, (b) correct the root cause of the error, and (c) error
compensation. Since it has been too expensive and requires a large effort to build a completely
accurate machine, the practical choices are either (b) or (c). The correction of the source(s) of the
errors requires each source to be isolated; then each error can be fixed one-by-one, or only the high
priority errors can be fixed, leaving the minor ones unresolved. The Taguchi method design of
experiments (Shahrom, Yahya, & Yusoff, 2013) is typical for type (b) problem-solving. The problemsolving process may take a significant amount of time when the problem is complicated as in a 4-axis
machine tool where there are 32 possible individual errors.
Y
X
B
Z
Table B
Spindle
Figure 1: Illustration of 4-axis B-table machine tool.
The third approach is just to correct the error or the phenomena without tracking down the
source(s) of the error. In CNC programming, this method is called compensation offset (Hai, Ni, &
Yuan, 1998). Furthermore, machines that have been in production use for a long period of time may
be less mechanically accurate if mechanical maintenance procedures are not strictly adhered to.
In the above example, the hole is measured by a CMM machine and has a location error ( x, y ) .
The compensation method simply offsets the machine tool coordinate by the opposite direction of the
error values (  x, y ) . Then the hole machined in the next cycle is accurate. The compensation
method is effective for any type of repeatable (consistent) error, including table error, fixture error,
spindle error or any other unknown errors.
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4 Error Compensation Offset Methods
The machine coordinate system (MCS) defines the home position of the axes. The work coordinate
system (WCS) defines the part location within the workspace. The WCS provides the origin and
orientation of a point selected either on the part or fixture; it can also be the same as the location of the
part coordinate system in the CAD. A tool path is programmed in the work offset coordinate system.
A part with multiple sides to be machined requires at least one WCS per side for machining or to
rotate the machine table to access all sides.
The machine offsets are used to define the relationship of the fixture and cutting tool from home
position. An offset coordinate system consists of nominal values and offset values for the part features.
The nominal values are the linear and rotary positions from the MCS. The offset is the adjustment to
improve part dimensional accuracy by taking into account varying tool length, table errors, fixture
errors, machine tool errors, etc. For example, it is difficult to manufacture a perfect fixture and/or
place the fixture at an exact location on the table, therefore, the offset is utilized to define its exact
location from the nominal position. There are several different types of work offset systems, as shown
in Fig. 2.
A part is located on the fixture using the manufacturing locators and then clamped down. The
fixture is installed on a rotary table. One of the manufacturing locators (or fixture center) is often a
round pin. The offset system (offset adjustment) is associated with a coordinate system positioned at
the fixture center. The majority of machine offsets are generally relative to the manufacturing datum in
Conventional
offset
Dynamic offset
Datum is the
manufacturing
locator. Either an
edge or locator
Global offset
Combined
Global and local
offset
Work offset
Coordinate
Discrete offset
Selective datum
Datum local
offset
Figure 2: Several types of offset coordinate systems.
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Gu et al.
order to consider all the machine tool system errors relative to the part print datum. On many
occasions, the part print datum for a number of features is not the same as the manufacturing datum. In
that case, a tolerance allocation analysis should be carried out, so that such features have in-process
tolerance (are adjusted) relative to the manufacturing datum. This approach is sufficient for the
majority of machined features.
In some cases, it is necessary to adjust a feature directly to a datum other than the manufacturing
datum. A common example is a pair of dowel holes used to locate one component to another. In that
case, the spatial relationship between the holes is critical and it may be necessary to offset the
secondary dowel hole relative to the primary dowel hole. The datum local offset strategy allows this
type of direct adjustment.
4.1 Conventional Offset System
Conventional offset is widely used in CNC machining industry and it is the current available offset
approach in machine tools. Conventional offset coordinate systems are used for individual part faces,
providing an individual offset for each part face. A conventional offset is defined for a group of
features in a single table rotary position. If the center of table rotation is not the program zero location
for each face, a separate program zero point will be assigned for each face. In addition, a face may
have more than one set of offsets. This, of course, means multiple face offsets will be required since
each face requires at least one set of three program zero assignment values ( X i , Yi , Z i ) .
Mathematically, a conventional offset is defined as,
 X i  x ni  x i

 Yi  y ni  y i
 Z  z  z
ni
i
 i
(Eq. 1)
Where ( X i , Yi , Z i ) is the coordinate system origin for each ith rotation/face, ( x ni , y ni , z ni ) are
the nominal values, and ( x i , y i , z i ) are the linear offsets.
For instance, consider a part that has features to be machined in three faces as shown in Fig. 3.
This part is machined in a 4-axis machine tool with B-rotary table using a single fixture. It has features
to be machined at table positions B1=0, B2 =90, and B3=270 as shown in Table 1. The features of milled
surfaces and drilled holes are identified as S and H, respectively.
B Table Rotary Feature Description
Position
B1=0o
S100,H101, H102
B2=90 o
S201,S202,H201H210
B3=270 o
S403, S405,H430
Coordinate
System
G54
G55
G57
Table 1: Features machined in various table rotary
positions
There are at least three sets of face offsets defined by the WCS G54, G55, and G57. The data
collected from features S100, H101 and H102 is used to calculate the offset for WCS G54. Likewise,
the data collected from features S201, S202 and H201-H210 is used to calculate the offset for WCS
G55. Finally, the data collected from features S403, S405 and H430 are used to calculate the offset for
WCS G57. The three WCS act separately and are compensated separately as shown in Table 2. A
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rotary offset Bi might be calculated for each face, but the calculation involves measurements from at
least two features. For instance, an angle adjustment can be calculated by dividing the difference
(measurements from two far apart points) by the distance. Also, the angle adjustments for each face
are different. Because these difficulties, the angle adjustment is typically omitted from conventional
offset. These face offsets ( x i , y i , z i ) are referred as “conventional offset” in this paper. This
method can be very time consuming because the programmer must calculate all of the offset values
from the part CMM data separately.
S100
H102
S201
S202
S403
H430
H201-H210
H101
B=270 FACE
B=0 FACE
B=0 FACE
S405
B=90 FACE
Figure 3: Example of a part’s machined features
B Table
Rotary Position
B1=00
B2=900
B3=270
Coordinate
System
G54
Conventional Offset
G55
0
G57
Table 2: Parameters of Conventional offset compensation
4.2 Dynamic Offset System
The location of the part on the fixture will result in at least some small error from the locating
features on the fixture to be mounted on the pallet. Fixtures are not always manufactured accurately
enough for perfect prediction of locating surface positions and its alignment on the table. Measuring
the position of locating surfaces on a new fixture, may show that the location surfaces do not precisely
match dimensions specified on the fixture drawing (but of course, the work holding device will still
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function properly). In addition, the part center may never match the table center of rotation. Of course,
the knowledge of the exact position of each location surface on the fixture from table center is most
important. As the table rotates, the fixture orbits around the pallet’s center and a new fixture offset is
required to create a suitable workpiece coordinate system.
Dynamic offset is a breakthrough in compensation theory (Fanuc, 2004) because it translates the
fixture coordinate system origin from table zero rotary position relative to the other table positions.
Regardless of which face of the workpiece is being machined, the programmed coordinates come from
the same place. In contrast to the conventional offset method, which treats each machined face as a
separate entity, the dynamic offset compensates all the machined features with a single set of offsets
( Px 0 , Py 0 , Pz 0 , B ) . These offsets are translated to each face for four program zero
assignment parameters (Wx i , Wy , Wz i , Wb ) .
The dynamic offset is defined by a rotational translation and it can be described as a system of
four equations:
Wx i  Tx  ( Px 0  Px 0 ) cos Bi  ( Pz 0  Pz 0 ) sin Bi

Wy i  Ty  Py 0  Py 0

Wz i  Tz  ( Px 0  Px 0 ) sin Bi  ( Pz 0  Pz 0 ) cos Bi

Wb  B
(Eq. 2)
Where
(Wx i , Wy , Wz i ) is the ith coordinate origin, Wb is the rotary offset for all the orientations;
Bi is the table nominal position for the ith workpiece orientation;
(Tx , Ty , Tz ) is the B-table linear nominal position and ( Px 0 , Py 0 , Pz 0 ) is the fixture linear
nominal position relative to the zero table rotary position B=0;
Px 0 , Py 0 , Pz 0 are the fixture offsets, respectively in the X, Y, and Z directions when B=0.
Considering the same example in Figure 3, the data collected from all the features machined in the
three faces is used to calculate the four offset parameters Px 0 , Py 0 , Pz 0 , B (see Table 3).
This method requires a perfect alignment of the table center otherwise the programmed coordinates
will not be correct. There is no easy way to deal with table position imperfections. The table center
may drift from its original position and cause a degradation in quality.
B Table Rotary
Position
B1= 0o
B2=90 o
B3=270
Coordinate
System
G54
Dynamic Offset
Parameters
G55
o
G57
Table 3. Parameters of Dynamic offset compensation
This method is not readily available since very few machine tool builders offer a rotary table
dynamic fixture offset compensation using G codes so that the operator can simply apply a work
coordinate offset adjustment and the control will track and update the part programmed points
dynamically in real time which takes into account the orbiting points of the rotary axis. The analysis is
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tedious because a spreadsheet is required (specific to the machine tool) to input the CMM data for the
part and estimate the four offset parameters for compensating the machine tool errors including fixture
location error.
4.3 Global Offset System
Global offset is an innovation built upon the dynamic offset by incorporating the table center errors
in compensation theory (US patent 8,676,373). All of the machined features are adjusted as a pattern
using six offset parameters; the global offset improves the part accuracy by considering all the quasistatic errors in a machine including the table and fixture errors. Global offset translates the table and
fixture coordinate system origin from table zero rotary position relative to the other table positions.
Optimal compensation is done through software, based on the part measurement data. Even though the
pallet is attached to the bed of the machine tool in a fixed pre-determined position using precision
locating cones in the base of the pallet, there is still an error in manufacturing the locating features in
the top plate of the pallet in relation to the locating cones. When the fixture is located on the pallet
using the fixed pre-determined locating features, the fixture errors are translated into workpiece
machining errors. The positioning repetitive indexing accuracy (consistency) of a pallet could be as
good as 0.002 mm but pallet errors including linear, angular, and flatness errors will be present. The
location of the part on the fixture will result in some small error due to manufacturing errors of the
locating features for fixture to pallet and part to fixture. It is impossible to align the part center to the
rotary axis. Therefore, the Global offset is developed to compensate all the errors present after a setup
is qualified within the machine tool. In addition, the Global offset can be used to compensate errors
that develop as the machine wears over time, or in the event of damage to the fixture or table.
The Global offset is defined by the following equations:
Wx i  (Tx  Tx )  ( Px 0  Px 0 ) cos Bi  ( Pz 0  Pz 0 ) sin Bi

(Eq. 3)
Wy  Ty  Py 0  Py 0

Wz i  (Tz  Tz )  ( Px 0  Px 0 ) sin Bi  ( Pz 0  Pz 0 ) cos Bi

Wb  B
Tx , Ty , Tz are the table center offsets in the X, Y, and Z directions to compensate the linear
table errors. Since the Y table error is collinear to the Y fixture error, the Ty is superimposed in the
fixture error and eliminated from Eq. 3. Therefore, the six offset parameters to be estimated in Eq. 3
are Px 0 , Py 0 , Pz 0 , Tx , Tz , B . These offset parameters are applied to the Global offset.
It is important to understand that at the B=0 rotary table position, the table and fixture offset errors
are easily superimposed because their coordinates are aligned with each other. However, when the
table rotates to positions other than B=0, the fixture/table offset coordinate system rotates a specified
angle Bi. In this case, the global offset is changing relative to the angle B i. The Global offset
incorporates both the fixture and table offsets through Eq. 3.
Referencing the part in Fig. 3 with features on three faces, the Global offset is determined for the
machine tool. The machining errors for each feature on the part are determined from the CMM
measurements. These errors are utilized in an algorithm that is discussed in a follow-up paper to
estimate the six parameters in Eq. 3. The model parameters are used to define the Global offset values
that are used to compensate each feature in the corresponding coordinate system as shown in Table 4.
Three offset coordinates are utilized for this part. The parameters for the G54, G55, and G57 are
defined by using Eq. 3 and respectively replacing angle B by B1=0, B2=90, and B3 =270. The
measurement data collected from all machined features is used in the Global offset Eq. 3 to estimate
the six parameters Tx , Tz , Px 0 , Py 0 , Pz 0 , B . Substituting these parameters in Eq. 3, the
Global offset compensates all three coordinate systems for all the features in the above example.
11
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
4.4 Global-Local Offset System
The Local offset is an additional refinement (fine adjustment) to the Global offset. It is a linear
offset that is applied locally to an individual feature or group of features and it does not consider
additional rotary error. The Local offset is defined by incorporating additional adjustment values in a
specific table angular position. Local offset provides additional flexibility to improve the dimensional
accuracy of certain part feature(s). Hence, it very effectively modifies the Global offset for specific
feature(s) with a tighter part print tolerance. It is expressed as:
B Table Rotary
Position
B1=0o
B2=90o
B3=270
Coordinate
System
G54
Global Offset Parameters
G55
o
G57
Table 4: Parameters of Global offset compensation
Wx ij  (Tx  Tx )  ( Px 0  Px 0 ) cos Bi  ( Pz 0  Pz 0 ) sin Bi  Lx j

Wy j  Ty  Py 0  Py 0  Ly j

(Eq.4)
Wz ij  (Tz  Tz )  ( Px 0  Px 0 ) sin Bi  ( Pz 0  Pz 0 ) cos Bi  Lz j
Wb  B

Where (Lx j , Ly j , Lz j ) is the Local offset, (Wx ij , Wy ij , Wz ij , Wb ) is the overall coordinate
offset for each feature, and j is the index for local offset.
The overall compensation value includes the Global and Local offsets for each coordinate
rotational position of the table/fixture and/or feature. The Global offset is obtained through a least
squares fit of all the equations generated by orginizing the CMM data for each of the part features in
Eq. 3. The Local offset value is the residual deviation value after the Global offset calculation. The
details of the algorithm are provided in a follow-up paper. More specifically, the Global offset will
compensate the repetitive quasi-static errors including table and fixture errors. It will also average out
some of the thermal (non-linear) errors and part to part variation if CMM data from several identical
parts is available. Local offset is intended to compensate as necessary for errors due to part and/or
fixture distortion, machine tool non-linear errors, etc.
For instance a few Local offsets can be assigned to a portion of the features for the part shown in
Fig. 3. First, assign a Local offset to the three features machined on face B 1=0. Then, assign a second
Local offset for features H201 and H210 on face B2=90. The remainder of the part features have
Global offset only. The procedure will use the CMM data for all part features to estimate the Global
offset for the part. Since all the features on face B1=0 are incorporated in a single Local offset, a single
G54 coordinate system is used to compensate these features as shown in Table 5. However, for face
B2=90, the Global offset is used to compensate all the features excluding H201 and H210 using the
coordinate system G55. The two features H201 and H210 utilize the Global offset together with the
Local offset in the coordinate system G56. Finally, the features on face B3=270 will use the Global
offset using the coordinate system G57.
12
CNC Machine Tool Work Offset Error Compensation Method
B Table Rotary
Position
B1 =0o
B2 =90 o
B2 =90
o
B3 =270 o
Coordinate
System
G54
Global Offset
Parameters
Gu et al.
Local Offset
Parameters
G55
G56
G57
Table 5: Parameters of Global and Local offset compensation
4.5 Discrete Offset System
There are many machine tools designed to accept work offset in a conventional method and/or a
separate linear offset for each individual table rotation. In this case, the Global offset system cannot be
utilized automatically. Therefore, a Discrete offset system is developed in this paper to accommodate
machine tools commonly found in manufacturing facilities. This ensures that the proper linear offset is
allocated to each table position. The Discrete offset is a form of combination Global and Local offset,
which translates the linear components of the Global offset into the corresponding linear offsets with
respect to table rotation positions to form the Discrete offset system. At least one set of linear offsets is
assigned to a given table position, unless Local offset is required for one or more features; in which
case, additional linear offsets are allocated. The model in Eq. 4 can be rewritten as
Wx ij  Tx  Px 0 cos Bi  Pz 0 sin Bi  x i  Lx j

Wy j  Ty  Py 0  y  Ly i

Wz ij  Tz  Px 0 sin Bi  Pz 0 cos Bi  z i  Lz j
Wb  B

(Eq. 5)
Where,
x i  Tx  Px 0 cos Bi  Pz 0 sin Bi

y  Py 0
z  Tz  Px sin B  Pz cos B
0
i
0
i
 i
and i and j represent the table rotation positions and the local offset index, respectively. If there are no
features with local offsets, the j subscript is neglected and (Lx j , Ly j , Lz j ) are zero.
For instance, consider the face B1=0 for the part in Fig. 3 with a Local offset assigned to all the
features. The Discrete offset for B=0 o is the superposition of the Global offset (that is translated to the
0 degrees position) and the Local offset shifted by G54 (see Table 6). Likewise, for the features on
face B2=90 without Local offset, the Global offset is translated by 90 degrees for the Discrete offset
G55 to compensate the errors. For the two features H201 and H210 on face B2=90 with Local offset,
the Discrete offset G56 is used as the sum of the Global offset translated by the 90 o position and the
Local offset. Finally, the Discrete offset G57 for the features on Face B3=270 rotation is obtained by
translating the Global offset by 270 o. The rotary error that affects all the table rotation positions
(squareness of the faces and features) is represented by the rotation component of the Global offset.
13
CNC Machine Tool Work Offset Error Compensation Method
B table Rotary Coordinate Global
Position
System
Offset
B1=0o
Gu et al.
Discrete Offset Parameters
G54
o
B2=90
B2=90 o
G55
G56
B3=270 o
G57
Table 6: Parameters of Discrete offset compensation
4.6 Datum Local Offset.
A Datum local offset is used to offset a group of features relative to a selected datum that could be
the manufacturing datum. In this case, the group of features must be in a same face (same table
position). The datum itself may be machined in the same operation as the offset feature(s), or may be
machined in a different operation. The adjustment is done in the coordinate system associated with the
manufacturing datum. The input measurement is relative to the selected part print datum. The Datum
local offset is described by equation (Eq. 6)
(Eq. 6)
Wx  DLx
DL

Wy DL  DLy
Wz  DLz
 DL
The Datum local offset corrects only for linear errors. It neglects possible angular error due to
misalignment between the measuring system and the manufacturing datum.
5 Error Compensation Verification on a Machine Tool
The Global Offset error compensation method has been rigorously tested and verified at a major
automotive company in the production of various transmission and engine components. It is important
that the compensation method is applied only if the machine’s volumetric accuracy is within a
specified range (i.e. 0.3 mm) and if it suffered a collision, it should be verified that it can still produce
dimensionally repeatable parts. The strategy behind this method is to utilize, because of its accuracy, a
CMM as a master gage and its accuracy should be several times or a magnitude better than the
compensation offsets. In addition, the uncertainty of the CMM should be better than the compensation
offset values.
5.1 Global versus Dynamic
A specific example of the effectiveness of the Global compensation method versus Dynamic
compensation method is illustrated here, with a 4-axis machine tool used to machine two bores and
drill several holes in an aluminum cylinder block. This machine is selected because it has a large table
center location error due to an accident. In this case, either the table must be repaired or the affected
14
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
machined features must be compensated. Since the mechanical repair would require several days or
even a week to perform, the Global offset compensation method is re-applied to compensate the
machine tool errors. A cylinder block is loaded on the fixture that sits on top of the table. Table 7 lists
the machined features along with the nominal value of the feature location. The features in Table 7
are machined in either the B table 0 or 180 degrees positions. The percent deviation of the actual
CMM values from the nominal values in relation to the feature tolerance [% Deviation = (Actual
Value – Nominal Value)/tolerance range] is provided in Figure 4. The average deviation in relation to
tolerances of the machined part is 47%, while the deviation for some of the features is as high as
100%. Therefore, the Global offset compensation can be used to reduce the errors. The CMM data
from a single part is loaded into an Excel-based Global offset calculation software (GCOMP) to
estimate the six parameters in Eq. 3. The estimated global offset parameters are provided in Table 8. A
simulation software is also developed based on Eq. 3 to calculate the theoretical corrected dimensional
values for the part features after the offset parameters are implemented, to provide the user the
estimated improvement in part quality. The optimization algorithm considers the objective function,
convergence criteria, number of equations available based on the machined/measured features,
regression functions to use, and method of optimization. The variation of model parameters continues
until one of the convergence criteria is met.
Part Feature Name
Nominal
Value
Actual Value Before
Compensation
Actual Value After
Compensation
Hole A - X
128.50
128.48
128.49
Hole A - Y
189.08
189.10
189.08
Hole B - X
Hole B - Y
-26.80
188.70
-26.78
188.72
-26.79
188.71
Hole C - X
41.00
41.05
41.01
Hole C - Y
295.50
295.52
295.50
Hole D - X
53.40
53.42
53.42
Hole D - Y
236.20
236.26
236.22
Chamfer E - Top
Chamfer E - Bot
415.67
437.77
415.80
438.06
415.58
437.83
Chamfer F - Top
300.71
300.86
300.66
Chamfer F - Bot
322.81
323.09
322.86
Chamfer G - Bot
77.19
76.91
77.13
Chamfer G - Top
99.29
99.16
99.34
Chamfer H - Bot
Chamfer H - Top
-44.79
-22.69
-45.06
-22.85
-44.87
-22.61
Chamfer I
-54.94
-55.18
-54.98
Table 7: Feature measurement data before and after global offset compensation
The simulation also predicted part dimensional errors as a percentage of the feature tolerance after
using the Global offset. The Global offset parameters in Table 8 are loaded into the CNC machine to
reduce the errors. Another part is then machined and measured in the CMM. The actual feature
15
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
location before targeting and after targeting using GCOMP are given in Table 7. Figure 5 shows the
CMM
Parameter
Global Offset Values
Dynamic Offset Values
ΔTx
ΔTz
0.03
-0.214
0
0
ΔPxo
0.008
0.007
ΔPyo
-0.023
-0.023
ΔPzo
-0.001
-0.025
ΔB
-0.01
-0.003
Table 8: Calculated Global offset and Dynamic offset model parameters
Figure 4: Comparison of Global and Dynamic offset compensation
data from the machined part with Global offset as compared to the simulation values. The data shown
in Figure 5 is based on two parts; the first part is used to calculate the offset parameters, the second
part is used to validate the accuracy of the offset parameters. The average difference among the
predicted and actual data is less than 1%. Figure 4 summarizes the ‘before’ and ‘after’ Global offset
measurement values. The average deviation of all the features machined in the operation is 14% with
Global offset as compared to 47% without compensation, a quality error reduction of 70%. The Min
deviation is reduced by 73%, while the Max deviation is also reduced by approximately 70%. It is
noted that the deviations of the actual and simulated values from the nominal may be positive or
16
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
negative, depending on whether the measurement value is above or below the nominal part print value
of the feature. For clarity, the absolute value of all deviations is shown in the graphs.
Figure 5: Comparison between simulations predicted improvement and actual improvement
The simulated deviation can be larger or smaller than the measured deviation of an actual
machined part because some of the dynamic machine tool errors including part to part variation are not
taken into account in the analysis of the Global offset especially if only one machined part is utilized
for estimation of the Global offset parameters. This is observed in Fig. 5. However, experience shows
that if the measurements of several machined parts are considered in the analysis, the actual measured
deviations after compensation will be smaller since the nominal part to part variation and some of the
dynamic errors will be included in the analysis. It can be observed that after compensating the errors,
the quality error is significantly reduced.
Using the previously mentioned predictive capabilities of the GCOMP software, it is possible to
test a scenario in which the machine is adjusted using the fixture linear moves and table rotary move
only, in other words, a Dynamic offset. As shown in Table 8, there is a significant table center
correction ΔTz prescribed by the GCOMP software. Table 8 provides the recommended offsets
without the table center adjustment as an active variable. The predicted improvement based on the
Dynamic offset parameters is shown in Fig. 4, along with the actual improvement provided by the
Global offset adjustment. It can be seen that in this case, the Global offset adjustment provided a
significant improvement in quality over the Dynamic offset adjustment. The improvement with the
Dynamic offset is very small since the major error source happened to be the machine table error. This
is because the machine in question has a significant table center error, on the order of 0.200 mm, and
the Dynamic offset is ineffective in this case. This clearly indicates the advantage of the Global offset
method over the Dynamic offset method.
17
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
The GCOMP is rerun with a Local offset applied to each of the three faces; in this case, the Local
offset doesn’t improve the predicted outcome significantly, so it is not included in the graphs and
tables.
5.2 Global-Local versus Conventional
The following example is used to illustrate the effectiveness of the Global-local compensation
method versus Conventional compensation method. In this case, a 4-axis CNC machine with C-table
is used to cut an array of 15 slots around a 150 mm bore in a part as shown in Fig. 6. The part is
located on a fixture on a rotary table and the bore is machined concentric to the table rotation axis so
that each slot is milled with a single axis of motion along the X-axis. The slots have equal spacing (24 o
apart).
S57
S58
S56
S55
S59
S54
S60
S53
S52
S46
S51
S47
S48
S49
S50
Figure 6: Machined slots in a part
One of the important control features is the location of the slot with respect to a specified location
on the bolt-circle. Therefore, the X locations (normal to the radius of the bolt-circle) error for each slot
is critical. A significant X position deviation is found after machining the first two parts as illustrated
in Fig. 7. The slots are listed consecutively according to their position in the circle. In addition, the
error is found to be repeatable among the two parts. The deviation ranges from -0.028 to 0.109 mm, a
significant variation and it has a bell shape. The specific machine has a significant rotary table error
that can be corrected either by physically repairing the problem or apply error compensation. It is also
observed that the error is not linear among the 15 slots. The non-linearity in the error of the symmetric
slots could be attributed to the table encoder, the distortion of the part under clamping, or tooling
pressure. The mechanical repair procedure (possibly replacing the encoder) is time-consuming, and
typically limited to an accuracy of approximately 10 microns. The distortion of the part due to
machining and/or clamping pressure is also complicated to address with simple fixture modifications
and few trials; the trial and error process would be extremely time consuming and may not fully
resolve the quality problem. Therefore, the error compensation approach could be satisfactory and a
better option, at least for the short term, as long as the compensation is sufficient to maintain the
spacing of the slots within the tight tolerance.
The conventional offset is the first compensation method applied to reduce the location error.
Additional parts are machined using the conventional offset. This method reduces the deviation range
from -75 micron to +51 microns, which shifts the bell shape to the center as shown in Fig. 7. This
indicates that the conventional offset averages the error among the 15 slots but there is no
improvement in the deviation range. This method shifts the mean but does not improve the variation.
Therefore, the Global offset is evaluated using Eq. 3. The global offset reduces the deviation range
18
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
from -0.042 microns to +0.021 mm, which reduces the range as well as shifts the bell shape to the
center as illustrated in Fig. 7. The Global offset offers obvious improvement over conventional offset,
since the deviation range is reduced by 50%. The shape of the graph still indicates a reflection point
and it seems that the shape of the deviations can be eliminated using the Global together with the
Local offset method. This is implemented using Eq. 4. The Global-Local offset reduces the deviation
range significantly (as illustrated in Fig. 7) and the bell shape is eliminated, indicating that the nonlinearity has been removed. The above example indicates that the Global offset can effectively
compensate the first source of error, while the Local offset compensates the second source of error. In
this case, the Local offset provides the swiftest and most accurate way to improve the quality.
.
Figure 7. Comparison among compensation methods for slot machining
6 Conclusion
The paper reports on several error compensation approaches using coordinate offset systems that
takes into account several aspects of the machine tool including table, fixture, and part errors during
machining. The core approach is the Global offset method. The compensation methods are evaluated
using the parts with features machined in multiple faces. These methods are suited for medium to high
volume production.
19
CNC Machine Tool Work Offset Error Compensation Method
Gu et al.
The proposed method aims to utilize the available part inspection data from production to improve
the quality of the part following the compensation method. It allows off-line error prediction and
compensation prior to executing the necessary changes through the machine controller for
compensation.
The results of the examples indicate the advantage of the Global-Local offset method over the
conventional and dynamic offset methods especially when the table and fixture locations have
significant errors including linearity of the axes encoders. In this case, the part is measured in an
inspection system (i.e. CMM) with respect to its locating (features) reference used in the machine
fixture to locate the part. The fixture location in the machine defines the part location relative to the
machine coordinate system. The inspection system records the part dimensional measurements. The
dimensional deviations between the measured part and the corresponding nominal part are calculated
by the inspection system. A compensation program is integrated with the inspection system to
translate the deviations to machine tool coordinate system offsets. The offsets are sent to the machine
tool controller so that the next machined part is compensated to minimize the part deviations caused
by geometric and thermal errors. The Global offset method adjusts all the controllable machine axes,
moving machined features on every face of the part as a pattern.
Finally, Global offset provides better quality over dynamic and conventional offset methods. The
Global offset has the flexibility to include local offsets, which allow fine adjustment of individual
features or small groups of features on a common face. The addition of Local offset allows reduction
of non-linearity caused by machine axes and part distortion caused by cutting and/or clamping forces.
The test results illustrate the effectiveness of the Global-Local Offset method.
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