Sources of error and uncertainty in

machine tool calibration

Dr Andrew Longstaff

Dr Simon Fletcher

University of Huddersfield

• Founded in 1825 • A history of education, innovation and

industrial collaboration

• Over 2,800 staff • 24,000 students • studying more than 400 degrees • An international University

• Students from over 130 countries • Delivering courses in China, Hong Kong,

India and Singapore

2

EPSRC Centre

• The EPSRC Centre for Innovative Manufacturing in Advanced Metrology

• based at the University of Huddersfield’s

• Centre for Precision Technologies,

• a long-established group with an international reputation in precision engineering and metrology research and development.

• Considering concept of the “factory on the machine”, we require elevation of machine tool accuracies

• hardware and software solution for stable metrology frame

• Efficient, traceable calibration

3

Machine tool error measurement Es

tab

lish

ed

• Artefacts/ self-centring probes

• Laser interferometry

• … C

urr

ent

SoA

• High accuracy laser trackers

• Sequential multilateration (TracCAL)

• Multi DoF lasers

• Ultra stable artefacts with scanning/optical probes

Futu

re

• Synchronised dynamic capture

• Affordable simultaneous multilateration

• Direct position feedback

• Continuous traceable adaptation

4

Volumetric Greater accuracy Faster

Subject of research work

Machine tool measurement

5

Main sources of uncertainty

• Some significant sources of uncertainty • Measurement methods

• Comprehensiveness of data • Measurement of all error sources

• Spatial resolution

• Finite stiffness

• Thermal deformation

• Errors due to motion

• Numerical compensation

6

Measurement methods

International Standards

• ISO 230 Test code for machine tools • Part 1: Geometric accuracy of machines operating

under no-load or quasi- static conditions

• Part 2: Determination of accuracy and repeatability of positioning numerically controlled axes

• Part 3: Determination of thermal effects

• Part 7: Geometric accuracy of axes of rotation

• Part 10: Determination of the measuring performance of a machine tool

• ISO 10791 Test conditions for machining centres

8

Fastest methods can increase uncertainty

• For example measurement of non-orthogonality between axes

• Using a “squareness artefact”

• Should be measured using two straightness measurements and least-squares fit

• Often measured with four points on a square.

9

Equipment effects

• Environmental factors and operator handling can induce thermal effects in instrumentation.

• In particular, angular and straightness interferometry is susceptible to

• thermal and

• mechanical stresses in the optics

• due to the sensitivity of the measurement to beam separation.

10

• Production constraints often mean that equipment is not given sufficient time to stabilise

• Without repeat measurement runs the drift would not be detected.

Comprehensiveness of data

Geometric error sources

• On a three-axis Cartesian machine there are the traditional “21” sources of geometric error • Some sources are simpler to

measure than others

• Some have such high measurement uncertainty that they are ignored

• On machines with parallel or rotary axes, the number of error sources increases • Neglecting to measure all sources

introduces uncontrolled uncertainty

B0 B180

Z+

Y+

12

Volumetric assessment

Decreasing omission of errors? or Increasing estimated uncertainty?

13

Spatial resolution

• Standard resolution measurement of vertical straightness

• shows some cyclic behaviour but

• may be mistaken as “noise”

• not obvious as a ballscrew issue

• Sparse data therefore increases uncertainty

• However length of test is increased by higher resolution

0 100 200 300 400 500 600 700 800 900 1000-50

0

50

Error (

m)

50mm steps

0 100 200 300 400 500 600 700 800 900 1000-50

0

50

Error (

m)

6.25mm steps

0 100 200 300 400 500 600 700 800 900 1000-50

0

50

Axis position (mm)

Error (

m)

4mm steps

14

Spatial resolution

• Example 0.5m machine axis • ISO targets efficient • For axes up to 2000 mm, a

minimum of five targets per 1000 mm and not less than 5 targets is required by ISO

• Error compensation applied on the machine using 10,20 and 50 targets

• Residual errors can be significant • Surface finish and form

• In reality the minimum is typically used • An effective option is filtering

15

0 50 100 150 200 250 300 350 400 450 500-8

-6

-4

-2

0

2

4

6

Axis position (mm)

Err

or

( m

)

ISO targets (10)

Improved targets (20)

Fine targets (50)

0 50 100 150 200 250 300 350 400 450 500-4

-3

-2

-1

0

1

2

3

Axis position (mm)

Err

or

( m

)

ISO targets (10)

Improved targets (20)

Smoothed data (20)

Reducing error through filtering

• The carriages/feet of an axis act as filters for high frequency imperfections

• Mathematical filters can

• better approximate this effect

• Improve noisy data from, for example, long range straightness data affected by air turbulence

• Technique also successfully applied to straightness error compensation

• However

• Over-filtering may omit real imperfections

16

Finite stiffness

Uncertainty from finite stiffness

• Long machine table

• Significant bend 200µm/m

• Uncertainty in • reading from a

laser interferometry

• Squareness of C axis to X

-100

-50

0

50

100

150

200

250

-3500 -3000 -2500 -2000 -1500 -1000 -500 0

Err

or

(mic

/m)

Axis position

Table bend

Level A

Level B

Laser

A B

Table

X axis +ve

EBX (X pitch error)

Fork head

18

Variation in mass on table

• The machine is often tested “unloaded” • Fixtures and the workpiece can have significant weight

• The distribution of the mass can cause distortion • Especially if table loads are mounted asymmetrically

• Own weight, fixture and workpiece mass variation affects geometry • Moving table example showed 90µrad increase in angular error with

1000Kg mass added.

Thermal deformation

Machine tool generic heat distributions

21

Carrier

Ball screw

Tool

Table

Base

Column Motor housing (internal heat source)

Bearings (internal heat source)

Belt drive

(internal heat source)

External heat entering the machine structure

Deformations of the machine results in tool displacement relative to the work piece

(Hence the thermal error)

Original machine profile Deformed machine profile Heat flow directions

Heat distribution

21

Environmental effect

• Traceability limited to conditions under which calibration made.

• Large 5-axis gantry in normal machine shop

(Late summer in northern Italy)

• Angular change 10µrad/C

• Straightness 11µm/ C

22

0 1000 2000 3000 4000 5000 6000 -20

-10

0

10

20

30

40

50

60

70

Axis position (mm)

Err

or

(µm

/m)

29.8ºC 26.1ºC 24.8ºC

0 1000 2000 3000 4000 5000 6000 -20

0

20

40

60

80

100

Axis position (mm)

Err

or

( m

)

29.3 ° C

24.8 ° C

Rapid change in temperature

• Rapid heating when cutting • Rapid cooling when not cutting

• For example probing

• Geometric measurements usually taken under nominally stable conditions

• Rapid error in spindle axial direction from • spindle speed change or • spindle stop

• Mechanical and thermal effect • Significant error between

spindle stop command and probing cycle start

0 20 40 60 80 100 120 140 160 180 200

0

10

20

30

40

50

60

Time (secs)

Movem

ent (

m)

Spindle stopped

M19

M5 Spindle stop

command

16µm/min

0 200 400 600 800 1000 1200 1400-250

-200

-150

-100

-50

0

50

100

150

Time (mins)

Movem

ent (

m)

Y

X

Z spindle

Z boss

23

Unforseen thermal effect

• Standard axis positioning error measurement • Poor repeatability compared

to expectation • Position monitored (EVE) • Cyclic error of >5µm • Due to underdamped air

chiller on the machine • Frequency dependent on the

environmental temperature • Time to complete

measurement approximately 22 minutes • Included just over 1 cycle

-4

-2

0

2

4

6

10 30 50La

se

r re

ad

ing

(m

icro

ns)

Time (minutes)

-2500 -2000 -1500 -1000 -500 0-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

ylinrepeatm.rtl

Axis position (mm)

Err

or (

m)

Repeatability > 9µm

24

Errors due to motion

Dynamic versus quasi-static

Dynamic data capture

• Dynamic data capture • Not convenient, since

actual and nominal positions must be synchronised.

• Rarely performed

• Bespoke system required

Rotary

Encoder

Z

Linear

Enc.

X AXIS UNCOMPENSATED ENCODER SIGNAL

Z AXIS UNCOMPENSATED ENCODER SIGNAL

Z AXIS COMPENSATED ENCODER SIGNAL

X AXIS COMPENSATED ENCODER SIGNAL

Encoder Interface

Compensation Cards

Geometric

Compensation

Computer

Z X

CNC Controller Z

X

X Axis Cross-rail

Machine

Measurement

Computer

Lase

r

inte

rfac

e

Enco

der

inte

rfac

e

Laser

26

Dynamic errors - measurement

• Cyclic errors and acceleration effects can be detected

• Dynamic effects can be different with varying • location on an axis

• speeds

• size of motion

• Therefore difficult to quantify

27

Numerical compensation

Numerical compensation

• Error compensation is the process of cancelling or correcting the effect of an error, usually by moving the axes of the machine.

• Can correct for errors that cannot easily be removed by error avoidance.

• Relatively inexpensive and easy to implement when compared to

mechanical realignment. • Flexible, since it can be updated to accommodate changes in error. • Is not intended as a substitute for good mechanical design and

build.

X Z

X0 X0 X0

(a) (b) (c)

Y

Correction

Error

29

Numerical compensation methods

• Internal (Controller)

• Part program modification

• Programmable Logic

Controller (PLC)

• Inbuilt pitch and cross-axis

• OEM application

• External

• PLC

• Feedback modification

• PC based

• Bespoke electronics

• Model types – commercially available

• Error map

• Simple linear expansion

• Parametric equations

• HTMs

• Model types – ongoing research

• Black box

• Artificial intelligence

30

Numerical compensation

• Electronic compensation is a powerful tool • Allows repeatable errors to be reduced without expensive

mechanical action

• But it introduces uncertainty, which varies depending • upon the skill of the engineer performing the update • the quality of the data • The quality of the compensation system • (An ISO standard is in preparation to help address this issue).

31 0 20 40 60 80 100 120 140 160 180 200

-40

-35

-30

-25

-20

-15

-10

-5

0

5

Time (Minutes)

Therm

al drift

(m

icro

n)

ANFIS Output

Thermal Error

Residual value

Simulation with measured data as a solution

Simulation of effects of errors

• Combining all machine error sources allows prediction of errors on probing (and machining) results • Magnitude and direction of errors represented by

arrows.

33

The future

• Measurement and simulation • dramatically reducing machine down-time for testing • simulate any conditions for more robust training

• seasonal environmental variations, • new running conditions for new products, • agile manufacturing.

Range of

conditions Machine

downtime

Range of conditions

Machine downtime

Present Ambition 34

Sources of error and uncertainty in

machine tool calibration

Thank you