**PERFORMANCE** **PARAMETERS** **METHODS** **INSTRUMENTS** **RECOMMENDATIONS** **ADVANTAGES**

**thermal error ****model**

*linear expansion of tool

*linear expansion of spindle

*linear expansion of columns

2-D analytical thermal model to evaluate thermal errors

and slope error. Thermocouples

**thermal ****positioning **

**errors**

*positioning error of the three axes of the machine

Analysis of thermal behaviour of machine tool, using thermocouples in specific positions, varying the operating

conditions and observing the effects on positioning error.

*32 t-Type thermocouple of foil construction

*data acquisition system

*controller through the RS-232 interface

*laser interferometer

*Thermocouples positions: in areas where there is maximum likelihood of obtaining a measurable change in temperature rise on account of subjecting the machine to the

different thermal cycles.

*These tests evidence the important point that the

thermal error of a machine tool is strongly

dependent upon the specific operating

parameters.

**thermal error ****model**

*11 error components are identified in different parts

of the machine tool

2-D error synthesis model to explain the positioning errors of the machine; co-ordinates frames are introduced and transformation matrices arrive at for each linkage. Error transformation is obtained as the difference between the

actual and desired tool position.

*80 thermocouples at various location are fitted up

*laser interferometer to evaluate 8 errors

*non contact capacitance sensors to evaluate 3 spindle errors

* to use materials like cement concrete, fibre reinforced plastics in the construction of the

machine tool; but it's expensive .

*It is imperative to keep the machine tool in a controlled ambient temperature rather than

have it exposed to the vagaries of the

atmosphere.

*One important suggestion is the use of temperature-controlled boxes.

** thermal error ****model**

*power losses in kinematics system components

*operational conditions (cutting power, operation time, ambient temperature,

spindle speed).

3-D thermal model of the machine tool is built with FEM; it also uses FEM to determine the temperature a distribution and the displacement on deformation. Assumption: the amount of energy dissipate in particular components of the

kinematics system is a function of the operational conditions.

*FEM

*Modelling the complete structure, the actual conditions of heat flow

could be adequately accounted for.

**thermal ****positioning **

**errors**

*length of a Telescopic Double Ball Bar

*Error vector of the machine tool

Measurement of changes of length of a Telescopic Double Ball Bar at multiple locations in the machine's working

volume while the machine is excited thermally. The machine's thermal behaviour can be determined throughout its working volume, by comparing measured

TDBB lengths performed at successive time intervals corresponding to a certain location in the machine's workspace to those measured lengths, determined when

starting a measurement. It is a 3-D method.

*Telescopic Double Ball Bar

*expansion free adapter (realised and designed by the author)

*magnetic socket for the connection with the workipece table and the machine's milling

head, respectively

*stand

*temperature sensor

*The TDBB length measurements can be executed in a few minutes due to the high measuring

speed of a TDBB.

**thermal ****positioning **

**errors**

*error on the axial depth of cut

Based on the consideration that for repeatable working conditions, the same temperature profile is generated, a

calibration of the thermal elongation of the spindle has been carried out for selected rotational speed. In order to do that a thermocouple is placed on the part of the spindle

surface where the highest temperature variations is detected, and a calibration curve is obtained.

*K-thermocouple

*A warm up of the spindle to the steady state temperature is required in order to assure the compatibility of the tool length value stored in the machine tool control with the actual one.

**thermal ****positioning **

**errors**

*positioning error along the Z-axis

The probe is mounted on the spindle box and a 1-D ball array is fixed on the working table. Initially, the coordinates of the balls are measured under cold-start conditions. Then

the spindle is run at a testing condition over a period of time to make the machine thermal status change. The thermal drifts of the tool are obtained by subtracting the

ball coordinates under the new thermal status from the referenced coordinates under cold-start conditions.

*1-D ball array gauge: series of balls with the same diameter and small sphericity

errors, fixed on a rigid base.

*probe

*Assumption: the friction of spindle bearings are the main heat source

**thermal ****positioning **

**errors**

*Relative displacement between the component that holds the tool and the component that holds the

work piece as a result of thermal expansion or contraction of key structural

elements.

The part of ISO 230-3 defines three tests, which are:

-ETVE (environmental temperature variation error test): to reveal the effect of the environmental changes on the

machine, and to estimate the thermally induced error during other performance measurements.

-Thermal distortion caused by rotating spindle test: to identify the effect to internal heat generated by rotation of

the spindle and the resultant temperature gradient along the structure on the distortion of the machine structure

observed between the work piece and the tool.

-Thermal distortion test caused by moving linear: to identify the effect of internal heat generated by the machine

positioning system on the distortion of the machine structure observed between the work piece and the tool in

the direction of travel.

*displacement measuring system: f.i.laser interferometer for moving linear axis, capacitive, inductive, retractable contacting

displacement sensors for environment testing and thermal distortion caused by

rotating spindle

*temperature sensors: f.i. thermocouple, resistance or semiconductor thermometer

*data acquisition equipment:f.i. multi- channel chart recorder, computer based

system

*test-mandrel ISO 230-1: 1996

*fixture to mount the displacement transducers

*If any hardware or software based compensation capability or facilities for minimizing thermal effects, such as air or oil

showers, are available on the machine tool they shall be used during the tests and the usage of these facilities shall be recorded.

*All dimensional measurement shall be made when the measuring instrument and the measured objects are in equilibrium with the environment where the temperature is kept at

20°. If the environment temperature is different, NDE (nominal differential thermal

expansion) correction between the measurement system and the measured object has to be made to correct the results to

correspond to 20°.

*It is a standard procedure

*It is easy for a general estimation of the thermal behaviour of the machine

**thermal ****positioning **

**errors**

*spindle thermal drifts:

three components of translational error and two components of rotational or

tilt errors.

It uses sequential trilateration to measure the spindle centre coordinates and spindle axis direction with respect

to the machine coordinate system

for various thermal states of the machine. The axial and radial thermal drifts are measured by computing the difference in spindle coordinates of the spindle centre at any thermal state from that at cold state. The tilt thermal drift is measured by computing the difference in the spindle

tilt at any thermal state from that at the cold state.

*Laser Ball Bar: displacement measuring laser interferometer aligned between two precision spheres by a telescoping tube

*magnetic socket

*It needs only one thermal cycle of the machine to

collect all the data.

*Because the LBB is removed during the warming period, all axes of the machine may be in

motion during the warming periods.

**static stiffness **

*Tool stiffness:

displacement of the tool tip

*Tool-holder stiffness:

displacement of the point where the force is applied

*Spindle stiffness:

displacement of the spindle's shaft

*Machine stiffness:

measurement of static stiffness in each direction.

Determination of the stiffness chain (machine+spindle+tool- holder+tool), with the application of a known load and the measurement of the ensuing deformation. Each element in

the system is measured independently, with specific, specially designed measuring methods being used in each

case. At the end, the real system has transformed into a system that behaves in an equivalent fashion, to evaluate

the total stiffness of the chain.

To apply the load: weight hung wire; pulley mechanism. To measure the displacement:

optical camera, a display

*It has been confirmed in experiments that tool- holder stiffness can vary considerably if experiments are not performed correctly.

*As tool diameter increases other elements must begin to be considered, especially the tool-holder (the assembly formed by the tool-

holder, the collect and the tool shank).

**static stiffness **

*Tool stiffness:

displacement of the tool tip

*Tool-holder stiffness:

displacement of the point where the force is applied

*Spindle stiffness:

displacement of the spindle's shaft

*Machine stiffness:

measured as the displacement of the spindle

nose with regard to the machine bed

Determination of the stiffness chain (machine+spindle+tool- holder+tool): the tool is fixture in the tool holder shank, the

displacement measuring sensors are installed, and the machine is proceeded to be pushed by the force measuring Kistler dynamometric plate. Once contact has

been established between the Kistler and the tool, a displacement is applied at a constant speed (very low) to the machine’s linear axis. Meanwhile, the displacement at

the sensor is measured at the same time as the force caused by the displacement of the dynamometer. At the end, the real system has transformed into a system that behaves in an equivalent fashion, to evaluate the total stiffness of the chain. A finite elements model of the tool has carried out too, to verify the validity of the equivalence

hypotheses on the system.

A Kistler dynamometer plate; inductive or capacitance sensors; amplifier; data

acquisition PC

The tool can be the most flexible link in the system in the case of very slender tools, but the influence of the rest of the system is very

important too.

* static stiffness * Stiffness of the machine
tool

Stiffness measurements are made by applying a force and measuring deflection

*Lion Precision capacitance gauge *tri- axial force sensors from Kistler (9018A and

9251A)

The machine stiffness needs to be improved in future prototypes to achieve mMT accuracy

goals given the magnitudes of inertial and cutting forces applied to machine structure

**dynamic effects**

Error in tool position in both the radial and the feed

direction

Effectiveness of the control process is presented in terms of its effect on the tool's acceleration before and after control. Which will reflect the effect of the machine-tool vibration on the tool. The dynamic model is describes in Laplace Domain and a Kalman estimator-based simulink

active control model simulates the machining process.

*Tefelon-D magnetostrictive transducer actuators *Simulink

The control process remains stable and drives

the tool's accelerations in both feed and radial direction to steady state.

**dynamic effects**

*following error as a function of acceleration for

each individual stage

Acceleration-based performance evaluation methodology:

is based on moves during which an individual stage undergoes constant acceleration from a stop up to the feed

velocity appropriate for that acceleration; the acceleration than changes sign and the stage returns to zero velocity.

During each move the following error (difference between the CNC controller command position and the feedback encoder actual position reading) is recorded and the data

are analyzed to determine the peak and RMS following error values. A calculation of relative accuracy as a function of acceleration can be performed based on evaluating the following error associated with an acceleration magnitude, determine the corresponding tool

size and calculating a relative accuracy between that following error and a feature size appropriate for the tool

size.

*Delta-tau Turbo PMAC2 controller: to send move commands to the machine (to obtain the desired acceleration profile) and capture

the optical encoder data

*Optical encoders from Micro-E System (M3500) and RSF Electronics (LIK 21): to

sense machine position.

*mathematical model for following error as a function of acceleration

*mMt design requirements can be determinated based on calculating the required bandwidth given a feature size and a

desired relative accuracy

*To achieve the requested bandwidth, a combination of reduced motor inductance, increased operating voltage, increased motor peak force and/or reduced stage moving mass

must be implemented.

**positional ****accuracy**

*squarenes

*linearity

*parallelism

Numeral-analytical accuracy calculation approach based on machined surfaces: modelling of the machined surfaces

by a form-shaping function and the machine tool as a chain of links.

*Mathematical knowledge

*machined part

*Construct the balance of accuracy of the machined

surface

*Elucidate the effect of individual factors of the accuracy of the machined

surface

*Predict the error sources from the results of measurements of the machined work piece on

the machine

**positional ****accuracy and **

**repeatability**

*Deterministic and stochastical values of geometric errors: 3 linear errors, and 3 angular errors

for each axis

After that the errors have been measured with the laser interferometer, they are analyzed with the rigid body kinematics model, considering the deterministic and the

stochastical values of each error.

*laser interferometer

**machine's ****accuracy model**

* geometric accuracy

*finite stiffness of the machine tool's components

*expansion coefficient of the machine tool's

components

*properties of the machine tool's slideways, joints

Uses of a so-called Individual Model (mathematical model), that describes the errors structure of an individual

machine tool at a certain time and place; this model is preceded by two intermediate models: the general, that

relates errors in the actual relative location of frames attached to tool and work piece to errors in the relative location of frames attached to succeeding components of the multi-axis machine, and type-dependent models, that relates the latter errors and the status of the machine and

its environment.

*Mathematical knowledge

**positional ****accuracy**

21 geometric errors, such as:

*linear motion error

*straightness error

*roll, pitch and yaw error

*squarenes error

*Description of a mathematical model to analyzed the 21 quasi-static error components of a three-axis machine tool

using homogeneous transformation matrices.

*Derivation of the parameterized error model and a practical methodology to estimate the quasi-static errors by

measuring 14 points along four body diagonals within the workspace based on the displacement approach.

*laser interferometer

*electronic levels

*capacitance gages

*The parametric model can reduce the calibration

time and cost because it requires the measurement data at only

14 positions from four body diagonal measurements

**positional ****accuracy**

21 geometric errors, such as:

*linear motion error

*straightness error

*roll, pitch and yaw error

*squarenes error

21 components errors need to be measured in order to calibrate its volumetric error. These errors are determined

with linear displacement measurement along 15/22 lines.

*laser interferometer

*electronic levels

*capacitance gages

*laser interferometer is the most widely used instrument for machine tool calibration because of

its accuracy

*with only 15 lines for the linear displacement

measurement, the measurement time is shorter, and the optics

used are less.

**positional ****accuracy**

*vertical and horizontal straightness for each axis

*pitch, roll and yaw for each axis.

Multi DOF system for measure 5 geometric errors components simultaneously along each axis of a mMTs.

The squarenes errors are determined by analyzing the slopes of straightness errors along orthogonal directions. It

measures totally 18 geometric errors, model by using last- squares fitting method/Homogeneous Transformation Matrices method. Considering these measurements, a

volumetric error model based on kinematics chain is derived to synthesize the geometric error components.

*fixture

*5 capacitance sensors of 250 µm measurements range, with resolution of 15

nm

*steel target with high surface finish

*In practice the following should also be considered while determining the machine

errors: (1) the effect of applied load; (2) accuracy of fixture and target; (3) error due to

mounting fixture.

*It can be implemented cost-effectively, without high cost accessories like

optics in laser interferometer.

*Because it is easy to setup and align, it can be

used more easily for assessment, calibration

and compensation of miniaturized systems

**positional ****accuracy**

21 geometric errors, such as:

*linear motion error

*straightness error

*roll, pitch and yaw error

*squarenes error

The machine is programmed to move on a circle and the deviations from an ideal circle are measured. The test requires a master piece in the form of a cylinder of which

measures about 6 points.

*touch-trigger

*simulation program

*It allows on-line testing

*It is a quick method of testing the accuracy (a complete test takes about

three hours).

**machine's ****accuracy**

*surface finishing

*geometric accuracy

Approach to compare the performance of very different types of machines. Machining trials consists of manufacturing 3 test pieces in three different materials on each of the machines. The test pieces are measured and

surface finish data recorded.

*Mitatoyo Euro 121210 Apex CMM: for measuring the test pieces

*Tallysurf Surtronic 3P: for measuring the surface finishing

*To contact the comparison a measurable test component is selected (ISO 10791-7 test

piece)

*This method is useful to make a comparison

between different machines.

**positional **

* accuracy* *linear motion error The laser interferometer measures the actual position of
the probe along the axis.

*laser interferometer

*linear interferometer

*retro reflector

*cube-corner

*laser card

*microcomputer

*this method of calibration is quite versatile

*Straightness of motion error: six elements of deviation, such as *one positional deviation in the

direction of motion *two linear deviation of the trajectory of a point on the moving component *three

angular deviation of a moving component

*Flatness error

a surface is deemed to be flat within a given range of measurement where all the points are contained within two

planes parallel to the general direction of the plane and separated by a given value. The general direction of the plane or representative plane in defined so as to minimize

the flatness deviation either:

*by three points conveniently chosen in the plane to be tested

or

*on a plane calculated from the plotted points by the least squares method.

*surface plate

*dial gauge

*precision level

*straightedge

*autocollimator

*sweep optical square

*laser measuring system

*coordinate measuring machine

*Squarenes

Squarenes measurements address the following points:

*squarenes of straight lines and planes: two planes, two straight lines, or a straight line and a plane are said to be perpendicular when the deviation of parallelism in relation to a standard square does not exceed a given value. The reference square may be a metrological square or a right-

angle level, or may consist of kinematics planes or lines.

*perpendicularity of motion: it refers to the successive point on a moving part of machine in relation to:

-a plane -a straight line

-the trajectory of a point on another moving part

*arm carrying a dial gauge

*Straightedge method: straightedge placed on two blocks, moving along it a dial gauge mounted on a support with one point on the line of the surface to be measured, and dial gauge stylus is on the line normal to the contact point and in contact with the straightedge.

*Tout-wire and microscope method: steel wire is stretched to be approximately parallel to the line to be checked with a microscope equipped with a micrometric displacement deviced that rears the deviation of the line to the taut-wire.

*Alignement telescope method: the difference in distance between the optical axis of the telescope and the mark shown on the target is read directly on the reticle or by means of the optical micrometer.

*Alignement laser tecnique: a laser beam is used as the reference of measurement, and the beam is directed at a four-quadrant photodiode detector which is moved along the axis of the laser C30beam.

**positional ****accuracy**

**DISADVANTAGES** **REFERENCES**
**[19]**

**[6]**

**[3]**

**[3]**

* Using an adapter to mount the TDBB beneath the milling head,

it could be introduce a measurement errors.

**[23]**

**[24]**

*[1] D.N. Reshetov, V.T. Portman, Accuracy of machine tools , *
New York: ASME, 1988.

*[2] C.H. Lo, J. Yuan, J. Ni, An application of real-time error *
*compensation on a turning centre , International Journal of *
Machine Tools and Manufacture 35 (12) (1995) 1669–1682
*[3] rR.Ramesh, M.A. MAnnan, A.N.Poo, Error compensation in *
*machine tools-a review. Part II:thermal errors , International *
Journal of Machine Tools and Manufacture, Volume 40, Issue
, 2000, Pages 1257-1284

*[4] Y.C. Shin, Y. Weit, A statistical analysis of positional errors *
*of a multiaxis machine tool , Precision Engineering, Volume 14, *
Issue 3, July 1992, Pages 139-146

[5] J. A. Soons, F. C. Theuws and P. H. Schellekens,
*Modelling the errors of multi-axis machines: a general *
*methodology , Precision Engineering, Volume 14, Issue 1, *
January 1992, Pages 5-19

*[6] R. Ramesh, M. A. Mannan and A. N. Poo, Thermal*
*error measurement and modelling in machine tools: Part*
*I. Influence of varying operating conditions ,International *
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Issue 4, March 2003, Pages 391-404.

*[7] Ji-Hun Jung, Jin-Phil Choi and Sang-Jo Lee,Machining*
*accuracy enhancement by compensating for volumetric *
*errors of a machine tool and on-machine measurement ,*
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Issues 1-3, 25 May 2006, Pages 56-66

*[8] Guiquan Chen, Jingxia Yuan and Jun Ni, A *
*displacement measurement approach for machine*
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Machine Tools and Manufacture, Volume 41,Issue 1,
January 2001, Pages 149-161

[9] Jenq Shyong Chen, Tzu Wei Kou and Shen Hwa Chiou
*Geometric error calibration of multi-axis machines using *
*an auto-alignment laser interferometer , Precision *

Engineering,Volume23,Issue 4,October 1999, Pages 243-252 [10] Jae Ha Lee, Yu Liu and Seung-Han Yang,

*Accuracy improvement of miniaturized machine tool:*

*Geometric error modeling and compensation ,*

International Journal of Machine Tools and Manufacture, Volume 46, Issues 12-13, October 2006, Pages

1508-1516

*[12] J.H. Lee and S.H. Yang, Measurement of geometric*
*errors in a miniaturized machine tool using capacitance*
*sensors , Journal of Materials Processing Technology,*
Volumes 164-165, 15 May2005, Pages 1402-1409
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L.N. Lopéz de Lacalle, A. Lamikiz and J. Albizuri,
*Error budget and stiffness chain assessment in a *
*micromilling machine equipped with tools less than 0.3*
*mm in diameter , Precision Engineering, In Press, *
Corrected Proof,Available on line 28 February 2006
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*Muñoa and J.A. Sánchez ,Evaluation of the stiffness chain*
*on the deflection of end-mills under cutting forces ,*

*It can be only used for Z-axis

positioning error. **[11]**

*The thermal drift is determined at a single, fixed position. As the

thermally induced drift of machine tool is position

dependent, and this measurement procedure has to be repeated at different locations

in the machine's workspace in order to determine the machine's

thermal behaviour.

**[22]**

*it needs an initialization procedure

*In the paper, it is only applied to a turning centre

**[15]**

**[13]**

*on the deflection of end-mills under cutting forces ,*
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*Gindy and K. Rask, A direct comparison of the machining*
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[20] Andrew G. Phillip, Shiv G. Kapoor and Richard E.

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*processes in both feed and radial directions using an *
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*[22] ISO 230-3, Test code for machine tools. Part 3: *

*determination of thermal effect , ISO, Geneva, Switzerland;*

2001

[23] F.L.M. Delbressine, G.H.J. Florussen, L.A. Schijvenaars
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*[25]ISO 230-1, Test code for machine tools. Part 1: Geometric*
*accuracy of machines operating under no-load or finishing *
*conditions , ISO, Geneva, Switzerland; 2001*

**[14]**

**[20]**

Interrupted cutting is difficult and involves impulse like forces that could cause chatter or instability

in the process

**[21]**

**[20]**

*too complicated and full of calculations for our purpose

*need of machined work piece

**[1]**

*it considers only 6 positional errors, instead of 11.

*it's too much complicated, for this work, apply this method to

the micro-machine tools.

**[4]**

*errors such as spindle-induced errors, tool misalignment, tool

wear, and thermal tool expansion are not directly

estimated.

*Only errors introduced by the machine are taken into account.

Errors in the location of the work piece with respect to the machine are not considered.

*The chosen nominal location of the various frames seriously affects the efficiency of the final

model.

*it is only a mathematical model, and it doesn't take into account

the real positional errors of the machine

**[5]**

**[7]**

*for different types of errors, different optics are required for

the measurement

*it cannot be used to measure the roll error

*measurement of the squarenes is complicated and difficult

**[8,9]**

*The squarenes error is not evaluate directly, but it is calculated from the straightness

errors.

**[10, 12]**

*Only the standard software package of the measuring machine should be used for the

measurements and the calculations.

*the master-piece requires specific characteristics.

**[16]**

*It can not be used to evaluate a single machine

*It requires a machined part

**[17]**

*This technique may be very time-consuming and labour intensive and may make the whole calibration process costly.

**[18]**

**[25]**