Catalog No. E11003(6)Mitutoyo Corporation
20-1, Sakado 1-Chome, Takatsu-ku, Kawasaki-shi,
Kanagawa 213-8533, Japan

Quick Guide to Precision Measuring Instruments

https://www.mitutoyo.co.jp

580 2112(6)g-(CH)NE-(JP11), Printed in JapanMitutoyo reserves the right to change any or all aspects of any product specification, including prices, designs and service content, without notice.

INDEX

Meaning of Symbols

02

Response to Safety and Environmental
Protection Regulations

03

Quality Control

04

Micrometers

06

Micrometer Heads

12

Inside Micrometers

16

Calipers

18

Height Gages

24

Depth Gages

28

Gauge Blocks

29

Dial Indicators, Digital Indicators and Test
Indicators

30

Linear Gages

35

Electronic Micrometers

39

Laser Scan Micrometers

40

Linear Scales

42

Profile Projectors

44

Microscopes

45

Vision Measuring Machines

47

Surftest (Surface Roughness Testers)

50

Contracer (Contour Measuring Instruments)

56

Roundtest (Roundform Measuring Instruments)

58

Hardness Testing Machines

62

Coordinate Measuring Machines

64

Quick Guide to Measurement

PG
01Meaning of Symbols

Response to Safety and Environmental Protection Regulations

ABSOLUTE Linear EncoderPG
02
is a trademark of
Mitutoyo Corporation.

This is an electronic measuring scale that provides a direct readout of absolute linear position when switched on, without needing to be zeroed or
reset. Mitutoyo measuring instruments incorporating these scales provide the significant benefit of being always ready for measurement without
the need of preliminary setting after switching on. There are three types of absolute linear encoders depending on whether the method used iselectrostatic, electromagnetic, or optical. They are widely used in various measuring instruments as measuring systems endowed with enhanced
reliability of measured values.
Advantages:
1. No count error occurs even if you move the slider or spindle extremely rapidly.
2. You do not have to reset the system to zero when turning on the system after turning it off*1.
3. As this type of encoder can drive with less power than the incremental encoder, the battery life is prolonged to about 5 years (continuous
operation of 18,000 hours)*2 under normal use.

Conformance to CE Marking

Response to WEEE Directive

In order to improve safety, each plant has programs to comply
with the Machinery Directive, the EMC Directive, and the Low
Voltage Directive. Compliance to CE marking is also met. CE
stands for "Conformité Européenne". CE marking indicatesthat a product complies with the essential requirements of therelevant European health, safety and environmental protection
legislation.

The WEEE Directive*1 is a directive that mandates appropriate
collection and recycling of electrical and electronic equipment
waste.
The purpose of this directive is to increase the reuse andrecycling of these products, and seeks eco-friendly productdesign.
To differentiate between equipment waste and household
is marked on awaste, a crossed-out wheeled-bin symbol
product.
We will promote eco-friendly design for our products.

*1: Unless the battery is removed.
*2: In the case of the ABSOLUTE Digimatic caliper (electrostatic capacitance model).

*1 WEEE Directive: Directive 2012/19/EU of the European Parliamentand of the Council on waste electrical and electronic equipment.

IP CodesThese are codes that indicate the degree of protection provided (by an enclosure) for the electrical function of a product against the ingress offoreign bodies, dust and water as defined in IEC standards (IEC 60529: 2001) and JIS C 0920: 2003.
[IEC: International Electrotechnical Commission]IP

is a trademark of Mitutoyo
Corporation.

SecondDegrees of protection against water
characteristic Brief description
Definition
numeral0

Unprotected—

0

Unprotected—

1

Protected against solid A Sø50 mm object probe
shall not fully penetrateforeign objects of
Sø50 mm and greater enclosure*1

Protected against
vertical water drops

Vertically falling water drops shall have noharmful effects.

2

Protected against solid A Sø12.5 mm object
probe shall not fully
foreign objects of
Sø12.5 mm and greater penetrate enclosure*2

Protected against
vertical water drops
within a tilt angle of
15°

Vertically falling water drops shall have noharmful effects when the enclosure is tilted
at any angle up to 15° on either side of thevertical.

3

Protected against solid A Sø2.5 mm object
probe shall not fully
foreign objects of
Sø2.5 mm and greater penetrate enclosure*3

Protected against
spraying water

Water sprayed at an angle up to 60° either sideof the vertical shall have no harmful effects.

4

Protected against solid A Sø1.0 mm object
probe shall not fully
foreign objects of
Sø1.0 mm and greater penetrate enclosure*4

Protected against
splashing water

Water splashed against the enclosure from any
direction shall have no harmful effects.

5

Protected against
water jets

Water projected in jets against the enclosure
from any direction shall have no harmful effects.

6

Protected against
powerful water jets

Water projected in powerful jets against theenclosure from any direction shall have noharmful effects.

7

Protection against
water penetration

Ingress of water in quantities causing harmful
effects shall not be possible when the enclosure
is temporarily immersed in water understandardized conditions of pressure and time.

6

Protected against dust

Dust-proof

REACH Regulation*2 is a regulation governing registration,
evaluation, authorization and restriction of chemical substancesin Europe, and all products such as substances, mixtures andmolded products (including accessories and packaging materials)
are regulated.
Chemical substances scientifically proven to be substances thatare hazardous to human health and the global environment(Candidate List of substances of very high concern for
Authorisation (CLS)) are prohibited to be sold or information
concerning them disclosed is mandated in Europe.
We will actively disclose information about our products andprovide replacement if we find our products contain any of thelisted substances.
*2 REACH Regulation: Regulation (EC) No1907/2006 of theEuropean Parliament and of the Council concerning theRegistration, Evaluation, Authorization and Restriction ofChemicals(IP: International Protection)

First
Degrees of protection against solid foreign objects
characteristic Brief description
Definition
numeral5

Response to REACH Regulation

Ingress of dust is not totally
prevented, but dust that
does penetrate must notinterfere with satisfactory
operation of the apparatus
or impair safety.
No ingress of dust allowed.

*: For details of the test conditions used in evaluating each degree of protection,please refer to the original standard.

8

Protected against the Ingress of water in quantities causing harmful
effects of continuous effects shall not be possible when the enclosure is
immersion in water continuously immersed in water under conditions
which shall be agreed between manufacturer anduser but which are more severe than for IPX7.

TÜV Rheinland certification marks
All products with the marks shown on the left have passed the IP test carried out by the German accreditation organization, TÜV Rheinland.

CONVENTIONS USED IN THIS BOOKLET

Conformity evaluation for CE marking (EMC Directives)

Major EU Directives relating to Mitutoyo products
Name of EU Directive
Machinery Directive

Applicable range
At least one part of a machine that may cause injury to thehuman body if it moves due to movement of an actuatorsuch as a motor.

EMC Directive (Electromagnetic A product that may produce electromagnetic
radiation or which is influenced by electromagnetic
Compatibility Directive)
radiation from outside.
Low Voltage Directive

Equipment (device) that uses AC voltage of 50 to 1000 V
or DC voltage of 75 to 1500 V.

Radio Equipment Directive

All electrical and electronic equipment that intentionallytransmits and receives radio waves at frequencies below
3000 GHz.

RoHS Directive

Restriction of the use of certain hazardous substances inelectrical and electronic equipment.
Our products fall under Cat.9 “Monitoring and control
instruments including industrial monitoring and control
instruments”.

Response to Management Methods for Restricted
Use of Hazardous Substances in Electrical andElectronic Product (China RoHS 2)
We set the environmental protection use period regulated by
China RoHS 2 per product and label with the marks shown on
the right, together with a list of the contained substances.

"Environmental Protection Use Period" mark*3*3 The environmental protection use period does not indicate theproduct warranty period.

The following symbols are used in this booklet to help the user obtain reliable measurement data through correct instrument operation.
correct

incorrect

Quick Guide to Measurement

PG
03

LSL
LSL

USL
USL

Quality Control
LSL
LSL

Quality control (QC)

Histogram

A system for economically producing products or services of a quality thatmeets customer requirements.

Activities to reduce variation in product output by a process and keep thisvariation low. Process improvement and standardization as well as technology
accumulation are promoted through these activities.

A diagram that divides the range between the maximum and the minimum
measurement values into several divisions and shows the number of values(appearance frequency) in each division in the form of a bar graph. This
makes it easier to understand the rough average or the approximate extent
of dispersion. A bell-shaped symmetric distribution is called the normal
distribution and is much used in theoretical examples on account of its easily
calculable characteristics. However, caution should be observed because many
real processes do not conform to the normal distribution, and error will result if
it is assumed that they do.

Statistical process control (SPC)

Process capability

Process quality control through statistical methods.

Process-specific performance demonstrated when the process is sufficiently
standardized, any causes of malfunctions are eliminated, and the process is ina state of statistical control. The process capability is represented by mean ±3
or 6 when the quality characteristic output from the process shows normal
distribution. (sigma) indicates standard deviation.

Process quality control

Population
A group of all items that have characteristics to be considered for improving
and controlling processes and quality of product. A group which is treatedbased on samples is usually the population represented by the samples.

Collection of product produced under the same conditions.

SampleAn item of product (or items) taken out of the population to investigate its
characteristics.

Process capability index (PCI or Cp)

Note: If a characteristic follows the normal distribution, 99.74 % data is within
the range ±3 from the mean.
Bilateral tolerance
USL-LSL
Cp = —
6

Sample size
Number of product items in the sample.

USL: Upper specification limit
LSL: Lower specification limit

Unilateral tolerance ... If only the upper limit is stipulated

Bias
Value calculated by subtracting the true value from the mean of measurement
values when multiple measurements are performed.

Variation in the values of a target characteristic in relation to the mean value.
Standard deviation is usually used to represent the dispersion of values aroundthe mean.
Upper specification limit (USL)

Mean

Target process mean

Cp = 1.33
6
68
8
LSL
LSL

USL
USL

X-R control chart
A control chart used for process control that provides the most information on
the process. The X-R control chart consists of the X control chart that uses themean of each subgroup for control to monitor abnormal bias of the process
mean and the R control chart that uses the range for control to monitor
abnormal variation. Usually, both charts are used together.

How to read the control chart
The process capability
is sufficient as it is no
closer than 2 sigma to thetolerance limits.

6
6
10
10

Note that Cp only represents the relationship between the tolerance limits andthe process dispersion and does not consider the position of the process mean.
Note: A process capability index that takes the difference between the process
mean from the target process mean into consideration is generally
called Cpk, which is the upper tolerance (USL minus the mean) divided
by 3 (half of process capability) or the lower tolerance (the mean value
minus LSL) divided by 3 , whichever is smaller.

Control chart

Typical trends of successive point position in the control chart that areconsidered undesirable are shown below. These trends are taken to meanthat a ‘special cause’ is affecting the process output and that action from theprocess operator is required to remedy the situation. These determination rules
only provide a guideline. Take the process-specific variation into consideration
when actually making determination rules. Assuming that the upper and thelower control limits are 3 away from the center line, divide the control chart
into six regions at intervals of 1 to apply the following rules. These rules areapplicable to the X control chart and the X control chart. Note that these 'trend
rules for action' were formulated assuming a normal distribution. Rules can beformulated to suit any other distribution.

UCL

Specific examples of a process capability index (Cp) (bilateral tolerance)
USL

The process capability isbarely achieved as the
6 sigma process limits
are coincident with thetolerance limits.

Cp = 1
6
LSL

2

3

4

5

(2) Nine consecutive points are to
one side of the center line.
X＋3
X＋2
X＋1

6

Subgroup number

7

X＋3
X＋2
X＋1

UCL

X

X
X−1
X−2
X−3

LCL

X−1
X−2
X−3

LCL

(3) Six points consecutively increaseor decrease.

Lower control limit (LCL)

X−1
X−2
X−3

LCL

(1) There is a point beyond either ofthe control limit lines (±3 ).

Upper control limit (UCL)

1

X
X−1
X−2
X−3

LCL

Used to control the process by separating the process variation into that due
to chance causes and that due to a malfunction. The control chart consists of
one center line (CL) and the control limit lines rationally determined above andbelow it (UCL and LCL). It can be said that the process is in a state of statisticalcontrol if all points are within the upper and lower control limit lines without
notable trends when the characteristic values that represent the process output
are plotted. The control chart is a useful tool for controlling process output,
and therefore quality.

X＋3
X＋2
X＋1

UCL

X

UCL

Unilateral tolerance ... If only the lower limit is stipulated

X＋3
X＋2
X＋1

UCL

Center line (CL)LSL
Lower specification limit (LSL)

The process capability is
the minimum value thatcan be generally accepted
as it is no closer than 1sigma to the tolerance
limits.

USL-X
Cp = —3

X-LSL
Cp = —
3

Dispersion, Imprecision

USL
USL

Cp = 1.67

The index value is calculated by dividing the tolerance of a target characteristic
by the process capability (6 ). The value calculated by dividing the difference
between the mean (X) and the standard value by 3 may be used to represent
this index in cases of a unilateral tolerance. The process capability index
assumes that a characteristic follows the normal distribution.

Lot

Frequency

PG
04

6
6

(4) 14 points alternately increase
and decrease.
X＋3
X＋2
X＋1

UCL

X＋3
X＋2
X＋1

X

X

X−1
X−2
LCL
X−3
(5) Two of three consecutive points are over
±2 from the center line on either side.

X−1
X−2
LCL
X−3
(6) Four of five consecutive points are over
±1 from the center line on either side.

Chance causes

UCL

These causes of variation are of relatively low importance. Chance causes aretechnologically or economically impossible to eliminate even if they can be
identified.

X

X

X−1
X−2
LCL
X−3
(7) There are 15 consecutive points within±1 from the center line.

X−1
X−2
LCL
X−3
(8) There are eight consecutive points over
±1 from the center line.

X＋3
X＋2
X＋1

UCL

X＋3
X＋2
X＋1

USL

Noncompliance

Bias

Measured values

68

Dispersion/imprecision
Tolerance (USL - LSL)

LSL

USL

6
10

Note: This part of 'Quick Guide to Precision Measuring Instruments' (pages 6 and 7) has been written by Mitutoyo based on its own interpretation of the JIS Quality
Control Handbook published by the Japanese Standards Association.
References- JIS Quality Control Handbook (Japanese Standards Association) Z 8101:1981
Z 8101-1:1999 Z 8101-2:1999 Z 9020:1999
Z 9021:1998

Quick Guide to Measurement

PG
05Micrometers
How to Read the Scale

Nomenclature

Micrometer with standard scale (graduation: 0.01 mm)
7. mm(1) Sleeve scale reading(2) Thimble scale reading + 0.37 mm

45

5

40

Anvil

35

Micrometer reading(2)

Note: 0.37 mm (2) is read at the position where the sleevefiducial line is aligned to the thimble graduations.

30

Frame

7.37 mm

The thimble scale can be read directly to 0.01 mm, as shown above, but may
also be estimated to 0.001 mm when the lines are nearly coincident because
the line thickness is 1/5 of the spacing between them.

ThimbleApprox. +1 µm

Thimble scale

Ratchet in speeder

Sleeve scale
Fiducial line
Thermally insulating plate

Digimatic Outside Micrometer08

Thimble scale

6
42

ThimbleRatchet in speeder

6
4
2

0

5

10

(1)

Frame

6. mm
(1) Sleeve scale reading
0.21 mm(2) Thimble scale reading(3) Reading from the vernier scale marking
and thimble graduation line
+ 0.003 mm
Micrometer reading
6.213 mm3025
20 (2)
15

8

Anvil

Note: 0.21 mm (2) is read at the position where the index line is between two
graduations (21 and 228 in this case).
30 0.003 mm (3) is read at the position
6
where one of the vernier
graduationsaligns with one of the thimble
25(3) 42
graduations.
(2)
20
0

Spindle clamp

Thimble scale
Sleeve scale
Output connector (not present in plain Digimatic model)

0

(1)

0

2

Special Purpose Micrometer Applications

0
45

0

(1)
9

Vernier reading 0.004mm (2)Fiducial line
Third decimal place
0.004mm (2)Second decimal place
0.09 mmFirst decimal place
0.9 mm (1)Millimetres
2. mm+ Tens of mm
00. mm Note: Indicates four digits.
Counter reading
2.994mm

Point micrometer

Note: 0.004 mm (2) is read at the position where a vernier graduation line
corresponds with one of the thimble graduation lines.

For inside diameter, and narrowgroove measurement

For small internal diameter, and For splined shaft diametergroove width measurement
measurement

Screw thread micrometer Disc type outside micrometer

Ball tooth thickness micrometer

For pipe thickness measurement

For root diameter measurement

Measuring Force Limiting Device

V-anvil micrometer

Audible inoperation

Onehanded Remarks
operation

Ratchet stop

Friction thimble(F type)Yes

Unsuitable

Audible clicking operation causes
micro-shocks

No

Suitable

Smooth operation without shock or
sound

Yes

Suitable

Audible operation provides
confirmation of constant measuring
force

Ratchet thimble

For effective thread diametermeasurement

For root tangent measurement on Measurement of gear over-pin
spur gears and helical gears.
diameter

For measurement of
3- or 5-flute cutting tools

14
13
12
11
10
9
8
7
6
5
4
3
2
1
0

300

200

100
50

2 4 6 810

15
20Time (minutes)

30

The above graph shows micrometer frame expansion due to heat transferfrom hand to frame when the frame is held in the bare hand which, as canbe seen, may result in a significant measurement error due to temperatureinduced expansion. If the micrometer must be held by hand during
measurement then try to minimize contact time. A heat insulator will reduce
this effect considerably if fitted, or gloves may be worn. (Note that the abovegraph shows typical effects and is not guaranteed.)

9mm

Tube micrometer

5

6
4
2

Origin button

Inside micrometer, caliper type Spline micrometer

5

Third decimal place on vernier scale ( 0.001 mm units)

ZERO (Incremental mode) / ABS(Absolute mode) setting button

Blade micrometer

Micrometer Expansion due to Holding Frame
with the Bare Hand

15
Micrometer with mechanical-digit display(digital step: 0.001 mm)
10

Display reading HOLD button

Thermally insulating plate

Note: The drawings above are for illustration only and are not to scale

Approx. +2 µm

30Index line
Thimble scale
25
(2)
20
5 (graduation:
Micrometer with vernier0 scale
0.001 mm)15
Index line

(3)

Fiducial line
SleeveCarbide tip(1)0

Measuring faces Spindle

Carbide tip

10 index line enables direct readings
The vernier scale provided above the sleeveto be made to within 0.001 mm.

Spindle clamp

30’

30’

spindle
ø8

0

ø7.95

Adjusting nut

spindleø6.35

SleeveExpansion (µm)

SpindleLength Standard Expansion with Change of
Temperature (for 200 mm bar initially at 20 ˚C)
Thermal expansion (µm)

PG
06

(1)

ø6.3

Standard Analog Outside Micrometer
Measuring faces

Measuring Face Detail

20

31°C

15
10

27°C

5
0

21°C
0

1

2

3

4

5

6

7

8

9

10

Lapse of time (minutes)

The above experimental graph shows how a particular micrometer standard
expanded with time as people whose hand temperatures were different(as shown) held the end of it at a room temperature of 20 °C. This graphshows that it is important not to set a micrometer while directly holding the
micrometer standard but to make adjustments only while wearing gloves orlightly supporting the length standard by its heat insulators.
When performing a measurement, note also that it takes time until the
expanded micrometer standard returns to the original length.
(Note that the graph values are not guaranteed values but experimental values.)

Quick Guide to Measurement

PG
07Micrometers
Abbe’s Principle

Three-wire method
The screw pitch diameter can be measured with the three-wire method
as shown in the figure.
Calculate the pitch diameter (E) with equations (1) and (2).

RθIn the above experiment, after the micrometer and its standard were left at a room
temperature of 20 ºC for about 24 hours for temperature stabilization, the startpoint was adjusted using the micrometer standard. Then, the micrometer with
its standard were left at the temperatures of 0 ºC and 10 ºC for about the same
period of time, and the start point was tested for shift. The above graph shows
the results for each of the sizes from 125 through 525 mm at each temperature.
This graph shows that both the micrometer and its standard must be left at thesame location for at least several hours before adjusting the start point. (Note thatthe graph values are not guaranteed values but experimental values.)

Hooke's Law
Hooke’s law states that strain in an elastic material is proportional to the stresscausing that strain, providing the strain remains within the elastic limit for thatmaterial.

Abbe’s principle states that “maximum accuracy is obtained when thescale and the measurement axes are common”.
This is because any variation in the relative angle ( ) of the moving
measuring jaw on an instrument, such as a caliper jaw micrometer,causes displacement that is not measured on the instrument’s
scale and this is an Abbe error ( = − L in the diagram). Spindle
straightness error, play in the spindle guide or variation of measuringforce can all cause ( ) to vary, and the error increases with R.

Hertz’s formula give the apparent reduction in diameter of spheres andcylinders due to elastic compression when measured between planesurfaces. These formula are useful for determining the deformation ofa workpiece caused by the measuring force in point and line contact
situations.
P

SøD

Changing the support method and/or orientation of a micrometer after zerosetting affects subsequent measuring results. The tables below highlight themeasurement errors to be expected in three other cases after micrometers are zeroset in the ‘Supported at the bottom and center’ case. These actual results show that
it is best to set and measure using the same orientation and support method.
Supporting method Supported at the bottom and center

Supported only at the center

Attitude

P
L

325
425
525
625
725
825
925
1025

Supporting method Supported at the center in a lateral orientation.
Attitude

Maximum
measuring
length (mm)
325
425
525
625
725
825
925
1025

−5.5
−2.5
−5.5
−11.0
−9.5
−18.0
−22.5
−26.0
Supported by hand downward.

øD

δ

(a)
(b)
Sphere between Cylinder between
two planes
two planes

Maximum possible
error
3 μm

−4.5
−10.5
−10.0
−5.5
−19.0
−35.0
−27.0
−40.0

Thread type
Metric thread or unified screw (60°)
Whitworth thread (55°)

Sm
E M

Screw

and, f = X
Z

Optimal wire size at D (P)
0.577
0.564

Precautions for eliminating errors
1. Correct the micrometer before use.

Error that might
not be eliminatedeven withprecautions±1 μm

Anvil angle error
Misaligned
contact points+10 μm+3 μm

1. Use a micrometer with a low
measuring force if possible.
Influence of±10μm
2. Always use the ratchet stop.
+3 μm
measuring force
3. Adjust the micrometer using a thread
gage with the same pitch.
1. Perform correction calculation (angle).
Angle error of
2. Correct the length error.
±10 μmthread gage
3. Adjust the micrometer using the same +3 μm
thread gage as the workpiece.
1. Perform correction calculation.
L
Length error of
2. Adjust the micrometer using the same ±1 μm± 3+ 25 μm
thread gage
thread gage as the workpiece.
1. Minimize the angle error as much as ±8 μm
JIS 2 grade error
half angle ±229 2. possible.
theWorkpiece thread of
Measure the angle error and perform assuming
minutes
error of half
angle error
correction
calculation.
-91 μmis ±23
3. Use the three-wire method for a large angle+71 μmminutesangle error.
Cumulative error)(±117+40) μm

Pitch error(workpiece)

Precautions for eliminating errors

Possible error

Error that might
not be eliminatedeven withprecautions

1. Correct the pitch error ( p = E)
µm assuming
2. Measure several points and adopt their ±18
that the pitch error
average.
is
0.02
mm.
3. Reduce single pitch errors.

Error of half angle 1. Use the optimal wire diameter.
(workpiece)
2. No correction is needed.
1. Use the optimal wire diameter.
Due to anvil
2. Use the wire which has a diameter
close to the average at the one wiredifferenceside.
1. Use the predetermined measuringforce appropriate for the pitch.
Wire diameter error 2. Use the predetermined width ofmeasurement edge.
3. Use a stable measuring force.

Formula for calculating a root tangent length (Sm):Sm = m cos 0 { (Zm − 0.5) + Z inv 0 } + 2 X m sin

0

Formula for calculating the number of teeth within the root tangent length (Zm):Zm' = Z·K (f) + 0.5 ( Zm is the integer closest to Zm'.)1
where, K (f) ={ sec 0 √ (1 + 2f) 2 − cos 2 0 − inv 0 − 2f tan 0}

Anvil

Major Measurement Errors of the Three-wire Method
Error cause

09P

d = Wire diameter
E = Screw pitch diameter
M = Micrometer reading including three wires
P = Screw pitch(Convert inches to millimeters for unified screws.)

Cumulative error

1. Measure the angle error and correct ±3 μm expected±5 μm assuming
micrometer.
measurement
the error of a half 2. theAdjust the micrometer using the same error of half
angle is 15 minutes thread
gage as the workpiece.
angle

(

+1.5
+2.0
−4.5
0
−9.5
−5.0
−14.0
−5.0

Assuming that the material is steel and units are as follows:
Modulus of elasticity: E =205 GPa
Amount of deformation:δ(µm)δ Diameter of sphere or cylinder: D (mm)2Length of cylinder: L (mm)δ
2 Measuring force: P (N)a) Apparent reduction in diameter of sphere3δ1=0.82 √P2/Db) Apparent reduction in diameter of cylinder3
δ2 =0.094·P/L √1/D

Major Measurement Errors of the Screw
Micrometer

Micrometer feed
error
0
0
0
0
0
0
0
0

2
2

Error cause
Maximum
measuring
length (mm)SpindleHertz's FormulaδEffect of Changing Support Method andOrientation (Unit: µm)

Metric thread or unified screw (60°)
E=M−3d+0.866025P .......(1)Whitworth thread (55°)
E=M−3.16568d+0.960491P .......(2)PG

d (×3)±3 μm±0.3 μm±0.3 μm

±8 μm

±1 μm

−3 μm

−1 μm

In the worst case
+20 μm−35 μmWhen measured
carefully
+3 μm
−5 μm

m : Module
0 : Pressure angle
Z : Number of teeth
X : Addendum modification coefficient
Sm : Root tangent length
Zm : Number of teeth within the root
tangent length

inv 20° 0.014904
inv 14.5° 0.0055448

Gear Measurement
Over-pin method

dp

dp

dm

ℓ

L ε

PG
08

Root Tangent Length

Screw Pitch Diameter Measurementdm

Difference in Thermal Expansion between
Micrometer and Length Standard

One-wire method
The pitch diameter of odd-fluted tap can be measured using the V-anvil
micrometer with the one-wire method. Obtain the measured value (M1)and calculate M with equation (3) or (4).
M1 = Micrometer reading during one-wire measurement
D = Odd-fluted tap diameter

(a)

(b)

For a gear with an even number of teeth:dg0dm = dp + cosø = dp + z·m·cos
cosø
For a gear with an odd number of teeth:dg0·cos 90°dm = dp + cos ø ·cos 90° = dp + z·m·cos
cos ø
z
z
however,
dp X
dp
0
·X
invø =–=–– inv 0 + 2tanzz·m·cos 0 2z
dg 2

( )

( )

)

(

Obtain ø (invø) from the involute function table.

Tap with three flutes : M = 3M1−2D ···························(3)Tap with five flutes : M = 2.2360M1−1.23606D ·······(4)Then, assign the calculated M to equation (1)or (2) to calculate the pitch diameter (E).

90º
Z

Anvil

z : Number of teeth
0 : Pressure angle teethm : Module
X : Addendum modification coefficient

SpindleOdd-fluted tap

Wire+26 μm-12 μmQuick Guide to Measurement

Micrometers
Testing Parallelism of Micrometer
Measuring Faces

Testing Flatness of Micrometer
Measuring Faces

Micrometer Performance Evaluation Method

Optical parallel reading direction on the spindle side

PG
10Interference fringe
reading direction

Optical parallel
Fringes on the spindle side

Parallelism can be estimated using an optical parallel held between the faces.
First, wring the parallel to the anvil measuring face. Then close the spindle
on the parallel using normal measuring force and count the number of red
interference fringes seen on the measuring face of the spindle in white light.
Each fringe represents a half wavelength difference in height (0.32 μm for red
fringes).
In the above figure a parallelism of approximately 1 µm is obtained from 0.32
µm x 3=0.96 µm.

Optical flat

Optical flat

Anvil

Anvil

Measuring face is curved by approximately
1.3 μm. (0.32 μm x 4 paired red fringes.)

Measuring face is concave (or convex) approximately 0.6
μm deep. (0.32 μm x 2 continuous fringes)

Fig. 1

General Notes on Using the Micrometer
1. Carefully check the type, measuring range, accuracy, and other specifications
to select the appropriate model for your application.
2. Leave the micrometer and workpiece at room temperature long enough fortheir temperatures to equalize before making a measurement.
3. Look directly at the fiducial line when taking a reading against the thimble
graduations. If the graduation lines are viewed from an angle, the correctalignment position of the lines cannot be read due to parallax error.

JIS B 7502 was revised and issued in 2016 as the Japanese Industrial Standardsof the micrometer, and the “Instrumental error” indicating the indication errorof the micrometer has been changed to “Maximum Permissible Error (MPE) of
indication”.
The “Instrumental error” of the conventional JIS adopts acceptance criteriathat the specification range (precision specification) equals acceptance range,
and the OK/NG judgment does not include measurement uncertainty (Fig.1).
The “Maximum Permissible Error (MPE) of indication” of the new JIS employs
the basic concept of the OK/NG judgment taking into account the uncertainty
adopted in the ISO standard (ISO 14253-1).
The verification of conformity and nonconformity to the specifications is clearlystipulated to use the internationally recognized acceptance criteria (simple
acceptance) when the specification range equals the acceptance range, and itis accepted that the specification range equals the acceptance range if a given
condition considering uncertainty is met.
The above said internationally recognized acceptance criterion is ISO/TR142536:2012 (Fig.2).
The following describes the standard inspection method including the revised
content of JIS 2016.

5. Wipe away any dust, chips and other debris from the circumference andmeasuring face of the spindle as part of daily maintenance. In addition,
sufficiently wipe off any stains and fingerprints on each part with dry cloth.
6. Use the constant-force device correctly so that measurements are performed
with the correct measuring force.
7. When attaching the micrometer onto a micrometer stand, the stand should
clamp the center of the micrometer frame. Do not clamp it too tightly.

Maximum Permissible Error of Full Surface
Contact Error J MPE [JIS B 7502: 2016]
The full surface contact error of the outside micrometer is an indication error
measured by contacting the entire measuring surface with the object to bemeasured at an arbitrary point in the measuring range.
The value can be obtained by adjusting the reference point using a constantpressure device with the minimum measuring length of the micrometer,
inserting a grade 0 or 1 gauge block prescribed in JIS B 7506 or an equivalentor higher gauge between the measuring surfaces (Fig. 3), and thensubtracting the dimensions of the gage block from the indication value of the
micrometer using a constant pressure device.

Gauge block

Conventional JIS Instrumental error
JIS B 7502-1994
Specification range
Conformity range

Non-conformity range

Non-conformity range

Fig. 3: M easurement of full surface
contact error

Acceptance range

(b)
(a)

Uncertainty is not included in judgment
Specification range ＝ Acceptance range(c)

SleeveThimble(a) From above the index line (b) Looking directly at the index line (c) From below the index line

4. W ipe off the measuring faces of both the anvil and spindle withlint-free paper set the start (zero) point before measuring.

New JIS Maximum Permissible Error (MPE)
JIS B 7502: 2016 (ISO/TR 14253-6: 2012)

Fig. 2
8. Be careful not to drop or bump the micrometer on anything. Do not rotate
the micrometer thimble using excessive force. If you believe a micrometer
may have been damaged due to accidental mishandling, ensure that it isinspected for accuracy before further use.
9. After a long storage period, or when there is no protective oil film visible,
lightly apply anti-corrosion oil to the micrometer by wiping with a cloth
soaked in it.
10. Notes on storage:
Avoid storing the micrometer in direct sunlight.
Store the micrometer in a ventilated place with low humidity.
Store the micrometer in a place with little dust.
Store the micrometer in a case or other container, which should not be kept
on the floor.
When storing the micrometer, always leave a gap of 0.1 to 1 mm between
the measuring faces.
Do not store the micrometer in a clamped state.

Specification range
Non-conformity range(Rejected )UU

Uncertainty
range

Conformity range
AcceptanceU

Non-conformity range(Rejected )U

Uncertainty
range

When a condition considering uncertainty is satisfied
Specification range ＝ Conformity range

Quick Guide to Measurement

PG

11Micrometer Heads

PG
12Key Factors in Selection

Constant-force Device

Ultra-fine Feed Applications

Key factors in selecting a micrometer head are the measuring range,
spindle face, stem, graduations, thimble diameter, etc.

• A micrometer head fitted with a constant-force device (ratchet or friction
thimble) is recommended for measurement applications.
• If using a micrometer head as a stop, or where saving space is a priority, ahead without a ratchet is probably the best choice.

Dedicated micrometer heads are available for manipulator applications, etc.,
which require ultra-fine feed or adjustment of spindle.

Stem
Plain stem

Stem locknut type• The stem used to mount a micrometer head is classified as a "plain type" or"clamp nut type" as illustrated above. The stem diameter is manufactured
to a nominal Metric or Imperial size with an h6 tolerance.
• The clamp nut stem allows fast and secure clamping of the micrometer
head. The plain stem has the advantage of wider application and slight
positional adjustment in the axial direction on final installation, although it
does requires a split-fixture clamping arrangement or adhesive fixing.
• General-purpose mounting fixtures are available as optional accessories.

Graduation Styles
0

5

45

25

20

0

Thimble Diameter

Micrometer head without constantforce device (no ratchet)Spindle Lock
If a micrometer head is used as a stop it is desirable to use a head fitted witha spindle lock so that the setting will not change even under repeated shockloading.

Measuring Face

Normalgraduation style

0

5

25

20

0 0

0
5

45

The diameter of a thimble greatly affects its usability and the "fineness" of
positioning. A small-diameter thimble allows quick positioning whereas a largediameter thimble allows fine positioning and easy reading of the graduations.
Some models combine the advantages of both features by mounting a coarsefeed thimble (speeder) on the large-diameter thimble.
Micrometer head withconstant-force device

20 80

10 90
5

90 10

Reversegraduation style

80 20

Bidirectional
graduation style• Care is needed when taking a reading from a mechanical micrometer head,especially if the user is unfamiliar with the model.
• The "normal graduation" style, identical to that of an outside micrometer, isthe standard. For this style the reading increases as the spindle retracts into
the body.
• On the contrary, in the “reverse graduation” style the reading increases as
the spindle advances out of the body.
• The "bidirectional graduation" style is intended to facilitate measurementin either direction by using black numerals for normal, and red numerals forreverse, operation.
• Micrometer heads with a mechanical or electronic digital display, whichallow direct reading of a measurement value, are also available. These types
are free from misreading errors. A further advantage is that the electronic
digital display type can enable computer-based storage and statisticalprocessing of measurement data.

Guidelines for Self-made Fixtures
Flat face

Spherical face

Anti-rotation device• A flat measuring face is often specified where a micrometer head is used inmeasurement applications.
• When a micrometer head is used as a feed device, a spherical face canminimize errors due to misalignment (Figure A). Alternatively, a flat face on
the spindle can bear against a sphere, such as a carbide ball (Figure B).
• A non-rotating spindle type micrometer head or one fitted with an antirotation device on the spindle (Figure C) can be used if a twisting action on
the workpiece must be avoided.
• If a micrometer head is used as a stop, then a flat face both on the spindle
and the face it contacts provides durability.
Figure A

Measuring Range (Stroke)

A micrometer head should be mounted by the stem in an accurately machined hole using a clamping method that does not exert excessive force on the stem. There arethree common mounting methods as shown below. Method (3) is not recommended. Adopt methods (1) or (2) wherever possible.
(Unit: mm)• When choosing a measuring range for a micrometer head, allow anadequate margin in consideration of the expected measurement stroke.
Six stroke ranges, 5 mm to 50 mm, are available for standard micrometerheads.
• Even if the expected stroke is small, such as 2 mm to 3 mm, it will be costeffective to choose a 25 mm-stroke model as long as there is enough spacefor installation.
• If a long stroke of over 50 mm is required, the concurrent use of a gauge
block can extend the effective measuring range. (Figure D)(1) Clamp nut

Mounting
method(2) Split-body clamp(3) Setscrew clamp

Figure C

Figure D
Gauge block

Figure B
Head’s stroke
Obtained stroke
Face A

Non-Rotating Spindle
A non-rotating spindle type head does not exert a twisting action on aworkpiece, which may be an important factor in some applications.

Spindle Thread Pitch• In this guide, the range (or stroke end) of the thimble is indicated by adashed line. For stroke ends, consider the thimble as moving to the positionindicated by the line when designing the jig.

Points to keep
in mindStem diameter
Mounting hole
Fitting tolerance

Precautions

ø9.5

ø10
G7
+0.005 to +0.020

ø12

ø18
G7
+0.006 to +0.024

ø9.5

ø10
G7
+0.005 to +0.020

ø12

ø18
G7
+0.006 to +0.024

Care should be taken to make Face A square to
Remove burrs generated on the wall of thethe mounting hole.
The stem can be clamped without any problem at mounting hole by the slitting operation.
squareness within 0.16/6.5.

ø9.5

ø10
H5
0 to +0.006

ø12

ø18
H5
0 to +0.008

M3x0.5 or M4x0.7 is an appropriate size for the
setscrew.
Limit countersinking into stem to 90°×0.5 and be
careful not to damage the stem in the process.

• The standard type head has 0.5 mm pitch.
• 1 mm-pitch type: quicker to set than standard type and avoids the possibilityof a 0.5 mm reading error. Excellent load-bearing characteristics due tolarger screw thread.
• 0.25 mm or 0.1 mm-pitch typeThis type is the best for fine-feed or fine-positioning applications.

Quick Guide to Measurement

PG

13Micrometer Heads
Maximum Loading Capacity of Micrometer Heads

Micrometer heads have applications in many fields of science and industry and Mitutoyo offers a wide range of standard models to meet customers’ needs. However,in those cases where the standard product is not suitable, Mitutoyo can custom build a head incorporating features better suited to your special application. Please feel
free to contact Mitutoyo about the possibilities - even if only one custom-manufactured piece is required.

The maximum loading capacity of a micrometer head depends mainly on the method of mounting and whether the loading is static or dynamic (used as a stop, forexample). Therefore the maximum loading capacity of each model cannot be definitively specified. The loading limits recommended by Mitutoyo (at less than 100,000
revolutions if used for measuring within the guaranteed accuracy range) and the results of static load tests using a small micrometer head are given below.

1. Spindle-end types
Standard

PG

4. Logo engraving

Spherical

PointedSplineTappedFlangedBlade (for non-rotating spindle
type only)Standard type

Couplings for providing motor drive to a head can be designed.

Long spindle type is also available. Please consult Mitutoyo.

2. Stem types

6. Thimble mounting

A custom stem can be manufactured to suit the mounting fixture.

Thimble mounting methods including a ratchet, setscrew, and hex-socket headscrew types are available.

Plain

Clamp nut

RatchetSetscrew

Hex-socket head screw(spindle pitch: 0.5 mm)
Spindle pitch: 0.1 mm/0.25 mm
Spindle pitch: 0.5 mm
High-functionality type Spindle pitch: 1.0 mm
Non-rotating spindle
MHF micro-fine feed type (with a differential mechanism)* Up to approx. 2 kgf only for MHT

Maximum loading limit
Up to approx. 4 kgf *Up to approx. 2 kgf
Up to approx. 4 kgf
Up to approx. 6 kgf
Up to approx. 2 kgf
Up to approx. 2 kgf

2. Static load test for micrometer heads (using 148-104/148-103 for this test)
Test method
Micrometer heads were set up as shown and the force at which the head was damaged or pushed out of the fixture when a static load was applied, in direction P, was measured. (In thetests no account was taken of the guaranteed accuracy range.)(1) Clamp nut
Threaded15

1. Recommended maximum loading limit

A specific logo can be engraved as required.

5. Motor Coupling(2) Split-body clamp(3) Setscrew clamp

FlangedPP

7. Spindle-thread pitch
3. Scale graduation schemes

Pitches of 1 mm for fast-feed applications or 0.25 mm and 0.1 mm for fine-feed
can be supplied as alternatives to the standard 0.5 mm. Inch pitches are also
supported. Please consult Mitutoyo for details.

Various barrel and thimble scale graduation schemes, such as reverse andvertical, are available. Please consult Mitutoyo for ordering a custom scheme
not shown here.

8. Lubricant for spindle threads

Clamp nut

SetscrewP
Split-body clamp

Lubrication arrangements can be specified by the customer.
Standard

Reverse
5

10

15

45

9. All-stainless construction00

All components of a head can be manufactured in stainless steel.

45

5

5

20

15

10. Simple packaging

5

5

5
0
45

45

Large-quantity orders of micrometer heads can be delivered in simple
packaging for OEM purposes.

05

Graduations only
0

10

15

20

5
45

0

15

10

Offset zero
10

10

Reverse vertical
5

Vertical

25

25

0

0

PG
14

Custom-built Products (Product Example Introductions)

Mounting method
Damaging / dislodging load*
Damage to the main unit will occur at 8.63 to 9.8 kN (880 to 1000 kgf).
(1) Clamp nut(2) Split-body clamp The main unit will be pushed out of the fixture at 0.69 to 0.98 kN (70 to 100 kgf).
(3) Setscrew clamp Damage to the setscrew will occur at 0.69 to 1.08 kN (70 to 110 kgf).
Note: These load values should only be used as an approximate guide.

11. Spindle and nut (Precision lead screw)
The spindle can be used as a precision lead screw. The nut is machined inaccordance with the specified dimensions.

12. Accuracy inspection certificate
An accuracy inspection certificate can be supplied at extra cost. For detailed
information, contact the nearest Mitutoyo Sales Office.

Quick Guide to Measurement

Inside Micrometers0.005 mm(1) Outer sleeve35(2) Thimble

0.015 mm

When a length standard bar or inside micrometer lies horizontally, supported
as simply as possible at two points, it bends under its own weight into a shapethat depends on the spacing of those points. There are two distances between
the points that control this deformation in useful ways, as shown below.

Reading

35.015 mm

Thimble5040Outer sleeve

35

(1)

10

(2)
45

mm

9

PG
16

Graduation

8

Cone

Airy and Bessel Points

7

Contact point

How to Read the Scale

Airy points (a0.577 )

Mitutoyo can custom-build an inside micrometer best suited to your special application. Please feel free to contact Mitutoyo about the possibilities - even if only one
custom-manufactured piece is required. Please note that, depending on circumstances, such a micrometer will usually need to be used with a master setting ring for
accuracy assurance. (A custom-ordered micrometer can be made compatible with a master ring supplied by the customer. Please consult Mitutoyo.)
スピンドル 外筒

シンブル ラチェットストップ

5

45

ℓ

When you use the tip of the anvil formeasurement, adjust the start point for
using the tip of the anvil.
Adjustment ofstart point

Contact point tip profile (example)r

H

W=0.5 or morera/N000000ødøD35-45mm

SplineTip radius R that can measure
the minimum diameter(different for each size)r

45˚ or more

/N000000

35-45mmød/N000000

35-45mmøD

Threaded
hole

X

ℓ

Figure 2

L: Inside diameter to be measured
L: Length measured with axial offset X
X: Offset in axial direction△ : Error in measurement△ : L− =√ 2+X2 −The change in length of a bar (or micrometer) due to bending can be
minimized by spacing the two supports symmetrically as shown above. These
points are known as the ‘Bessel Points’ and may be useful when using a longinside micrometer.

: Inside diameter to be measured
L: Length measured with radial offset X
X: Offset in radial direction△ : Error in measurement△ : L− =√ 2–X2 −• Reference point setting with a ring gage or cylinder master gage
Insert the bore gage into the ring gage, vertically or horizontally swing thebore gage, and set the zero point to the point where the indicator reads the
maximum value. (Rotate the dial face for a dial gage and perform presettingor zero setting for a Digimatic indicator.)• Reference point setting with outside micrometer and gauge block
Hold a gauge block (of the reference dimension) between a micrometer’smeasuring faces as if measuring the block. Clamp the micrometer's spindle
and then pull out the gauge block. Insert the bore gage between the
micrometer’s measuring faces. Maneuver the bore gage to the position
where the indicator reads a minimum and then set the pointer to read zero (ora preset value required) by rotating the bezel.
• Reference point setting with outside micrometer only
Fix the micrometer in a vertical attitude with its head side (spindle side)
downward (see illustration below), and then adjust the distance between
the measuring faces to the reference dimension. At this time, do not clamp
the micrometer spindle. Insert the bore gage between the micrometer’smeasuring faces. Maneuver the bore gage to the position where theindicator reads a minimum and then set the pointer to read zero (or a preset
value required) by rotating the bezel. Zero-setting with a micrometer requires
a certain degree of dexterity because no self-centering action is available, as
is the case when using a setting gage.
Zero-setting is also possible by performing the same procedure using thegauge block, height master, or bore gage zero checker in addition to theoutside micrometer.

If the Inside Micrometer is misaligned in the axial or radial direction by an
offset distance X when a measurement is taken, as in Figures 1 and 2, thenthat measurement will be in error as shown in the graph below (constructedfrom the formula given above). The error is positive for axial misalignment andnegative for radial misalignment.

R=0.3 or moreøDSerration

X

Figure 1

L• Allows measurement of the diameter of variously shaped inside grooves andsplines.
• Minimum measurable groove diameter is approximately 16 mm (differs
depending on the workpiece profile.)• Dimension should be as follows:
For W = less than 2 mm: = less than 2 mm
• For W = 2 mm or more: = 2 mm as the standard value which can be
modified according to circumstances.
• The number of splines or serrations is limited to a multiple of 3.
• Details of the workpiece profile should be provided at the time of placing acustom-order.
• If your application needs a measuring range different from that of thestandard inside micrometer an additional initial cost for the master ring gage
will be required.

ℓ35-45mm

H/N000000

ød

øD

Round
grooveTip radius R that can measure W=1 or more R=0.5 or more
the minimum diameter(different for each size)• Allows measurement of the effective diameter of an internal thread.
• Measurable internal threads are restricted according to the type, nominal
dimension, and pitch of the thread. Please contact Mitutoyo with thespecification of the thread to be measured for advice.

Error (positive for axial,
and negative for radial,
misalignment) (mm)r

Effect of misalignment on accuracy(Inside Micrometer)/N000000

35-45mm

ødH2

H1

W=1 or more

The accuracy of an inside micrometer is degraded if its temperature issignificantly different from. To help prevent this situation occurring wear gloves
and only hold the micrometer by the heat insulators to reduce the transfer ofheat from the operator's hands.

øD

SquaregrooveTip radius R that can measure
the minimum diameter(different for each size)

Remarks

0.559 )

Reference point setting (2-point gages)

Measurement error due to temperatureeffects on an inside micrometer
Workpiece profile (example)

Bessel points (aaWorkpiece

Type offeatureThe ends of a bar (or micrometer) can be made exactly horizontal by spacing
the two supports symmetrically as shown above. These points are known as the‘Airy Points’ and are commonly used to ensure that the ends of a length bar
are parallel to one another, so that the length is well defined.

50When Holtest is used, the measured value
differs between measurement across the anvil
and the measurement only at the tip of theanvil due to the product mechanism.
Adjust the start point under the same condition
before measurement.

45

Custom-ordered Products (Holtest / Borematic)

45

コーン

Changes in measured values at different
measuring points
1DIV. 0.005mm

Ratchet45

Thimble1DIV. 0.005mm

測定子

Sleeve0aSpindle

0

0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01

PG

17

ℓ

6

Nomenclature (Holtest)

1 2 3 4 5 6 7 8 9 10
Misalignment (offset) of one end of micrometer (mm)Quick Guide to Measurement

Calipers

PG
18

Nomenclature

Measurement examples

Vernier Caliper

Outside measurement

Inside measurement
Measuring faces

PG

19

Screw, gib setting

Inside measuring faces
Step measuring faces

Gib, slider
Locking screw
Screw, gib pressing

Depth bar
Stopper, slider

BeamMeasuring faces
Inside jaws
Outside jaws

Main scale

Thumbwheel

Step measurement

Depth measuring faces

Reference surface

Depth measurement

Measuring faces

Vernier scale
SliderOutside measuring faces

Measuring faces

Absolute Digimatic Caliper■ How to Read the Scale●Vernier Calipers①

0Inside measuring faces
Step measuringMainscale faces
Locking screw
Slider10

20

30●Dial Calipers

40

Output connector

90

0.01mm

70
60

1

2

3

4

5

6

7

8

9

30

(2)

505-666

10

20

10
20

MADE IN JAPAN

50

70

(2)

0.01mm

70

Beam

30

505-66660
80

70

MADE IN JAPAN

(1)

10
0

0

10

20
0

1

30
2

(2)

3

4

40
5

6

50
7

8

9

60

1

30
2

3

4

40
5

6

50
7

8

9

60

(2)

(1) Main scale(2) Vernier
Reading

(1)

90

0

10

80

10

20

0

0.01mm700505-6661016mm
0.15 mm
16.15 mm

For stepped feature measurement

For depth measurement

10

Blade jaw type

Neck type

Tube Thickness typeFor diameter of narrow groove
measurement

For outside diameter measurement suchas thickness of recess

For pipe thickness measurement

20

60

MADE IN JAPAN

50

(2)

(2)
30

0.01mm70505-666

10

60

30

MADE IN JAPAN

70

50

70

40

40

Main scale

Main scale

0.05 mm080

70Dial faceVernier scale

Graduation

For uneven surface measurement

Dial Calipers

70

10Depth type

Depth measuring faces

90

20

Offset jaw type

Dial face(1)0

Point jaw type

Main scale

10

InsideVernier scale
jaws
Reference surface
Main scale
OutsideThumb-roller
Graduation
0.05 mm
Graduation
0.01 mmjaws
ZERObutton(1) Main scale reading(1) Main scale reading
16mm
4.00 Set/ABSOLUTEmm(2) Vernier scale reading(2) Dial face reading
0.13 mm0.75 mm
Dial Caliper reading
16.13 mm
Caliper reading
4.75 mm
Outside measuring faces

Vernier Calipers

Depth bar

40

50

40

②

How to Read the Scale■ How to Read the Scale

Special Purpose Caliper Applications

10

80

0

80

0

0

0

90

(1)

Graduation(1) Main scale(2) Dial face
Reading

0.01 mm16mm
0.13 mm
16.13 mm

Note: Above left, 0.15 mm (2) is read at the position where a main scale graduation line corresponds with a vernier graduation line.

Quick Guide to Measurement

Calipers
Small hole measurement with an M-type caliper

This is a short auxiliary scale that enables accurate interpolation between
the divisions of a longer scale without using mechanical magnification. The
principle of operation is that each vernier scale division is slightly smaller than amain scale division, so that successive vernier graduations successively coincidewith main scale graduations as one is moved relative to the other. Specifically,n divisions on a vernier scale are the same length as n‑1 divisions on the main
scale it works with, and n defines the division (or interpolation) ratio. Althoughn may be any number, in practice it is typically 10, 20, 25, etc., so that thedivision is a useful decimal fraction. The example below is for n = 10. The main
scale is graduated in mm, and so the vernier scale is 9 mm (10 divisions) long,the same as 9 mm (9 divisions) on the main scale. This produces a difference inlength of 0.1 mm (1) as shown in figure A (the 1st vernier graduation is alignedwith the first main scale graduation). If the vernier scale is slid 0.1 mm to theright as shown in figure B, the 2nd graduation line on the vernier scale moves
into alignment with the 2nd line on the main scale (2), and so enables easy
reading of the 0.1 mm displacement.

A structural error d occurs when you measure the internal diameter of a smallhole.
øD: True internal diameterød : Measured diametert1, t2: Thickness of the inside jaw
C: Distance between the inside jaws
d: Measurement error (øD–ød)фD

8. Maintenance of beam sliding surfaces and measuring faces
Wipe away dust and dirt from the sliding surfaces and measuring faces with adry soft cloth before using the caliper.
2. Inside measurement
Insert the inside jaw as deeply as possible before measurement.
Read the maximum indicated value during inside measurement.
Read the minimum indicated value during groove width measurement.

ødøD(1) 0.1 mm
Divided into10 equal divisions

Inside Measurement with a CM-type Caliper

3. Depth measurement
Read the minimum indicated value during depth measurement.

Because the inside measuring faces of a CM-type caliper are at the tips of theBjaws the measuring face parallelism is heavily affected by measuring force, andthis becomes a large factor in the measurement accuracy attainable.
0.1 mmIn contrast to an M-type caliper, a CM-type caliper cannot measure a very small
hole diameter because it is limited to the size of the stepped jaws, althoughSome early calipers divided 19 divisions on the main scale by 20 vernier divisions
normally this is no inconvenience as it would be unusual to have to measure
to provide 0.05 mm resolution. However, the closely spaced lines proved difficulta very small hole with this type of caliper. Of course, the radius of curvature
to read and so, since the 1970s, a long vernier scale that uses 39 main scaleon the inside measuring faces is always small enough to allow correct holedivisions to spread the lines is generally used instead, as shown below.
diameter measurements right down to the lowest limit (jaw closure).
•1
 9 mm Vernier scale•3
 9 mm vernier scale(long vernier scale)
Mitutoyo CM-type calipers are provided with an extra scale on the slider
for50inside60 measurements
so they can be read directly without the need for
0
10
20
30
40
30
40 0 50 10 6020 7030
40
30
40
70
calculation, just as for an outside measurement. This useful feature eliminates
0.05 mm0.05mmthe possibility of error that occurs when having to add the inside-jaw-thickness
0 2 4 6 8 10
0 1 2 3 04 25 4 6 6 7 8 810 9 10
0 1 2 3 4 5 6 7 8 9 10
correction on a single-scale caliper.
Scale reading 30.35 mm

39

4. Parallax error when reading the scales
Look straight at the vernier graduation line when checking the alignment ofvernier graduation lines to the main scale graduation lines.
If you look at a vernier graduation line from an oblique direction (A), theapparent alignment position is distorted by X as shown in the figure below
due to a parallax effect caused by the step height (H) between the planes of thevernier graduations and the main scale graduations, resulting in a reading errorof the measured value. To avoid this error, the JIS stipulates that the step heightshould be no more than 0.3 mm.

H

A

About Long Calipers
Steel rules are commonly used to roughly measure large workpieces but if alittle more accuracy is needed then a long caliper is suitable for the job. A longcaliper is very convenient for its user friendliness but does require some care inuse. In the first place it is important to realize there is no relationship between
resolution and accuracy. For details, refer to the values in our catalog.Resolution
is constant whereas the accuracy obtainable varies dramatically according to
how the caliper is used.
The measuring method with this instrument is a concern since distortion of
the main beam causes a large amount of the measurement error, so accuracy
will vary greatly depending on the method used for supporting the caliper at
the time. Also, be careful not to use too much measuring force when using
the outside measuring faces as they are furthest away from the main beam soerrors will be at a maximum here. This precaution is also necessary when using
the tips of the outside measuring faces of a long-jaw caliper.

H

ΔX

For outside only

General notes on use of caliper
1. Potential causes of error
A variety of factors can cause errors when measuring with a caliper. Major
factors include parallax effects, excessive measuring force due to the fact that acaliper does not conform to Abbe's Principle, differential thermal expansion due
to a temperature difference between the caliper and workpiece, and the effectof the thickness of the knife-edge jaws and the clearance between these jaws
during measurement of the diameter of a small hole. Although there are also
other error factors such as graduation accuracy, reference edge straightness,main scale flatness on the main blade, and squareness of the jaws, these factors
are included within the instrumental error tolerances. Therefore, these factors
do not cause problems as long as the caliper satisfies the instrumental error
tolerances. Handling notes have been added to the JIS so that consumers canappreciate the error factors caused by the structure of the caliper before use.
These notes relate to the measuring force and stipulate that “as the caliper
does not have a constant-force device, you must measure a workpiece with anappropriate even measuring force. Take extra care when you measure it withthe root or tip of the jaw because a large error could occur in such cases.”ødøD

Close jaws
completely

Battery

10. Handling after use
After using the caliper, completely wipe off any water and oil. Then, lightly
apply anti-corrosion oil and let it dry before storage.
Wipe off water from a waterproof caliper as well because it may also rust.
11. Notes on storage
Avoid direct sunlight, high temperatures, low temperatures, and high humidity
during storage.
If a digital caliper will not be used for more than three months, remove thebattery before storage.
Do not leave the jaws of a caliper completely closed during storage.

For inside only

Calipers were made that gave an even finer resolution of 0.02 mm. These
required a 49-division vernier scale dividing 50 main scale divisions. However,they were difficult to read and are now hard to find since Digital calipers withan easily read display and resolution of 0.01 mm appeared.

ORIGIN

5. Moving Jaw Tilt Error
If the moving jaw becomes tilted out of parallel with the fixed jaw, either
through excessive force being used on the slider or lack of straightness in thereference edge of the beam, a measurement error will occur as shown in the
figure. This error may be substantial due to the fact that a caliper does notconform to Abbe’s Principle.

f = hθ = h aaScale reading 1.45 mm

19
39 mm

ORIGIN button sets display to zero

ℓ

h

19 mm

9. Checking and setting the origin before use
Clean the measuring surfaces by gripping a sheet of clean paper between theoutside jaws and then slowly pulling it out. Close the jaws and ensure thatthe vernier scale (or display) reads zero before using the caliper. When using a
Digimatic caliper, reset the origin (ORIGIN button) after replacing the battery.

h(2) Aligned

7. Handling
Caliper jaws are sharp, and therefore the instrument must be handled with careto avoid personal injury.
Avoid damaging the scale of a digital caliper and do not engrave an
identification number or other information on it with an electric marker pen.
Avoid damaging a caliper by subjecting it to impact with hard objects or bydropping it on a bench or the floor.

L < фD

C t2

9 mm (9 graduation lines)

A

6. Relationship between measurement and temperature
The main scale of a caliper is engraved (or mounted on) stainless steel, andalthough the linear thermal expansion coefficient is equal to that of the mostcommon workpiece material, steel, i.e. (10.2 ±1) ×10-6 / K, note that otherworkpiece materials, the room temperature and the workpiece temperature
may affect measurement accuracy.

L

True internal diameter (øD: 5 mm) Unit: mm
t1+t2+C
0.3
0.5
0.7
d
0.009
0.026
0.047

t1

PG
20

Vernier scalef

Example: Assume that the error slope of the jaws due to tilt of the slider is 0.01 mm in 50 mm andthe outside measuring jaws are 40 mm deep, then the error (at the jaw tip) is calculated as(40/50)x0.01 mm = 0.008 mm.
If the guide face is worn then an error may be present even using the correct measuring force.

Quick Guide to Measurement

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21

Calipers

PG
22

Performance evaluation method for the caliper

Scale Shift Error S MPE [JIS B 7507: 2016]

Support for ISO 13385-1:2019

Shift Error S (MPE)

JIS B 7507 was revised and issued in 2016 as the Japanese Industrial Standardsof the caliper, and the “Instrumental error” indicating the indication errorof the caliper has been changed to “Maximum Permissible Error (MPE) of
indication”.
The “Instrumental error” of the conventional JIS adopts acceptance criteriathat the specification range (precision specification) equals acceptance range,
and the OK/NG judgment does not include measurement uncertainty. (Fig. 1)
The “Maximum Permissible Error (MPE) of indication” of the new JIS adopts
the basic concept of the OK/NG judgment taking into account the uncertainty
adopted in the ISO standard (ISO 14253-1).
The verification of conformity and nonconformity to the specifications is clearlystipulated to use the internationally recognized acceptance criteria (simple
acceptance) when the specification range equals the acceptance range, and itis accepted that the specification range equals the acceptance range if a given
condition considering uncertainty is met.
In this case, the internationally recognized acceptance criterion is ISO/TR
14253-6:2012. (Fig. 2)
The following describes the standard inspection method including the revised
content of JIS 2016.

The scale shift error in a caliper is an indication error of the inside measurement,
depth measurement, etc., if measuring surfaces other than the outside
measuring surfaces are used.
The Maximum Permissible Error SMPE of the indication value for insidemeasurement is given in Table 1. The Maximum Permissible Error SMPE of depth
measurement is obtained by adding 0.02 mm to a value in Table 1.
The indication error for inside measurement can be obtained by using gauge
blocks (or equivalent standards) and standard jaws from an accessory set toform accurate inside dimensions for calibration (Fig. 4), with the error being
given by the indicated value minus the gauge block size.

The ISO standard for calipers, ISO 13385-1, was revised and published as ISO
13385-1:2019 in August 2019. The major point of this revision is that it more
specifically quantifies the notation and the inspection methods, etc. related
to caliper accuracy. This quantification does not affect the quality of calipers
manufactured in the past, as they were measured and inspected in an agreed,
standardized way in line with certain methods and criteria. The following
paragraphs explain points and changes in the revised ISO 13385-1:2019.

The Shift Error for calipers is the error of indication for areas other than theoutside measuring face. In the ISO-2019 standard, all measurement errors(inside, depth, step, and I.D. measurement error) other than the outside
measurement error (EMPE) are Scale Shift Errors (SMPE). Test points and their
number were newly quantified as the type of errors included in the Scale Shift
Error were better specified. (Fig. 2, 3, Table 3)

Fig. 1conventional JIS Instrumental error
JIS B 7507-1993

Unit: mm
Scale interval, graduation or resolution
Measurement length
0.05
0.02
50 or less
± 0.05± 0.02
Over 50, 100 or less
± 0.06± 0.03
Over 100, 200 or less
± 0.07
Over 200, 300 or less
± 0.08± 0.04
Note: E MPE includes the measurement error arising from the straightness, flatness andparallelism of the measuring surface.
Table 1: Maximum Permissible Error E MPE of partial measuring surface contact error in aconventional caliper.

(Fig. 2)

Partial surface contact error E (MPE)
The partial surface contact error of a caliper is an indication error applied tooutside measurement.
The ISO-2019 standard quantifies for each measuring range the testing method
and criteria, such as test points, number of tests, and testing arrangement thatwere previously left to the manufacturers’ own criteria.
(Fig. 1, Table 1)Ex.) F or a caliper with a measuring range of 150 mm, the revised standard
requires five or more test points.
(Fig. 1)Ex.) Step and depth measurement(Table 3)[ISO 13385-1:2019]
Test numbering Test point Reference standard
Less than 50 mm Gauge block１

Scale Shift Error measurement exampledepth measurement(Fig. 3)Specification range
Conformity range

Non-conformity range

Non-conformity range

Scale Shift Error measurement examplestep measurement

Acceptance range

Uncertainty is not included in judgment
Specification range ＝ Acceptance range

New JIS Maximum Permissible Error (MPE)
JIS B 7507: 2016 (ISO/TR 14253-6: 2012)

Fig. 2Gauge block
Fig. 3: Determining of partial measuring surface contact error

U

U

Uncertainty
range

Conformity range
Acceptance

U

150
300
1000
1000 or more

5
6
7
8

For example, for depth measurement or step measurement, the standard
specifically requires one or more test points at less than 50 mm and a testingarrangement using gauge blocks.
(See Table 3)

Gauge block

Furthermore, the revised standards require testing in 90% or more points
within the product measuring range as well as testing at the root and tip of thejaw at the maximum/minimum point. Therefore, it is important to conduct tests
following the newly defined standard.
The following is an example of measurement for a 150 mm caliper. To comply
with the ISO-2019 standard, the minimum number of test points is five for a
150 mm caliper. (Table 1)
Five or more test points are necessary to comply with the ISO-2019 standard.
These include testing at the maximum and minimum point, as well as at theroot and tip of the measuring unit. These test points must add up to a totalof five.

Specification range
Non-conformity range(Rejected )Number of partial surface contact error test points (Table 1)
Measuring range (mm)Minimum number of test points

Non-conformity range(Rejected )U

Uncertainty
range

When a condition considering uncertainty is satisfied
Specification range ＝ Conformity range
Fig. 4: Determining inside measurement indication error

Maximum Permissible Error of partial measuring
surface contact error EMPE [JIS B 7507:2016]
The partial measuring surface contact error of a caliper is an indication error
applied to the outside measurement.
Table 1 shows the Maximum Permissible Error E MPE of the indication value ofthe partial measuring surface contact error.
The value can be obtained by inserting a gauge block, or an equivalent or
higher gauge, between the outside measuring surfaces (Fig. 3), measuring
the different position along the jaw at an arbitrary position in the measuring
range and then subtracting the dimension of the gage from the indicatedvalue.

Quick Guide to Measurement

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23

Height Gages
Nomenclature

How to read

Vernier Height Gage

Mechanical Digit Height Gage

PG
24

Vernier Height gage

Fine adjuster for main scale

5

Sub pole

Column

4

(2)

7

6

Column

2

80 20

(1)

Fine adjustment device
Clamp
Locking device

Counter, upward
Counter, downward
Hand-pointer
Dial face

Scribing stylus

Measuring face,stylusFixing device

Measuring face,stylusFixing device(2) Dial

0.11 mm

Reading122.11 mm

3060

8 7 8 mm

40

50

50

1 2 2 mm

Reference surface

7

Measuring downwards from a reference surface

Main scale

Vernier scale

Reference surface

Graduation

0.02 mm(1) Main scale

79.00 mm(2) Vernier

0.36 mm

Reading

79.36 mm(1) Counter 125.00 mm
90

0
0

10

80 20

10

90

80 20

0.01mm8 7 5 mm(2) Dial

0.11 mm

Reading

125.11 mm

125.11
70 30

70
40

60

60
50

50

40

30

1 2 5 mm

Base

Base

Digimatic Height Gages

General notes on use of Height Gages
Strut

f

ColumnSlider handwheel

Preset mode, ball diametercompensation mode button

2. Reference edge (column) warping and scriber installationah height gage if the reference column, which guides the slider, becomes
Like the caliper, and as shown in the following figure, measurement errors result when using thewarped. This error can be represented by the same calculation formula for errors caused by nonconformance to Abbe's Principle.
Installing the scriber (or a lever-type dial indicator) requires careful consideration because it affects the size of any error due to a warped reference column by increasing
dimension h in the above formula. In other words, if an optional long scriber or lever-type dial indicator is used, the measurement error becomes larger.

Power ON/OFF key
Zero set button/ABS (Absolute) button
Hold/data button

1. Potential causes of errorhLike the caliper, the error factors involved include parallax effects, error caused by excessive measuring force due to the fact that a height gage does not conform toAbbe's Principle, and differential thermal expansion due to a temperature difference between the height gage and workpiece.
There are also other error factors caused by the structure of the height gage. In particular, the error factors related to a warped reference edge and scriber installation
described below should be studied before use.
l

Main poleSub pole

Touch probe connector
Measuring andscribing stylus
Battery cap
Stylus clamp

40

Scribing
stylusReference surface, base

80 20

70

7

(1)

10

90

70 30
60

Reset button

00.01mm90Feed handle
SliderMeasuring andscribing stylus
Stylus clamp

Stylus clamp
Measuring andscribing stylus
Scribing stylus

Feed handle
Slider

122.11

1

Locking device

0

10

1

10

2

Main scale

90

9

0

Reference surface, beam
Reference surface, base(1) Counter 122.00 mm

11
5

4

PG

Scribing stylus

10

3

3

Carrier
SliderVernier scale

Measuring upwards from a reference surface

11

Main pole

Beam

Mechanical Digit Height gage

6

Strut

Digimatic data socket

Slider clamping lever

Number up/down button, presettinghf

Scribing stylus

Direction switch/digit shift button,presettinglMeasuring face, stylus

Ergonomic base

Fixing devicea

Base
Reference surface, basehhf =h =ha

Example: Effect of measuring point position
When h is 150 mm, the error is 1.5 times larger thanwhen h is 100 mm.

lf

Height gage applications with optional accessories and other measuring toolshaTest indicator attachment

Touch probe attachment

Center probe attachment

Depth gage attachmenthQuick Guide to Measurement

25

Height Gages

PG
26

3. Lifting of the base from the reference surface
When setting the scriber height from a gauge block stack, or from a workpiecefeature, the base may lift from the surface plate if excessive downwards force isused on the slider, and this results in measurement error. For accurate setting,move the slider slowly downwards while moving the scriber tip to and fro overthe gauge block surface (or feature). The correct setting is when the scriber
is just felt to lightly touch as it moves over the edge of the surface. It is also
necessary to make sure that the surface plate and height gage base reference
surface are free of dust or burrs before use.

Notes on using the height gage

Height Gage Performance Evaluation Method

1. Keep the column, which guides the slider, clean. If dust or dirt accumulates
on it, sliding becomes difficult, leading to errors in setting and measuring.

JIS B 7517 was revised and issued in 2018 as the Japanese Industrial Standardsof the height gage, and the “Instrumental error” indicating the indication
error of the height gage has been changed to “Maximum Permissible Error(MPE) of indication”.
The “Instrumental error” of the conventional JIS adopts acceptance criteriathat the specification range (precision specification) equals acceptance range,
and the OK/NG judgment does not include measurement uncertainty (Fig. 1).
The “Maximum Permissible Error (MPE) of indication” of the new JIS employs
the basic concept of the OK/NG judgment taking into account the uncertainty
adopted in the ISO standard (ISO 14253-1).
The verification of conformity and nonconformity to the specifications isclearly stipulated to use the internationally recognized acceptance criteria(simple acceptance) when the specification range equals the acceptance
range, and it is accepted that the specification range equals the acceptance
range if a given condition considering uncertainty is met.
The above said internationally recognized acceptance criterion is ISO/TR
14253-6: 2012 (Fig. 2).
The following describes the standard inspection method including the revised
content of JIS 2018.

2. When scribing, securely lock the slider in position using the clamping
arrangements provided. It is advisable to confirm the setting after clamping
because the act of clamping on some height gages can alter the setting
slightly. If this is so, allowance must be made when setting to allow for thiseffect.
3. Parallelism between the scriber measuring face and the base reference
surface should be 0.01 mm or better.
Remove any dust or burrs on the mounting surface when installing thescriber or lever-type dial indicator before measurement. Keep the scriber andother parts securely fixed in place during measurement.
4. If the main scale of the height gage can be moved, move it as required to
set the zero point, and securely tighten the fixing nuts.
5. Errors due to parallax error are not negligible. When reading a value, always
look straight at the graduations.
6. Handling after use: Completely wipe away any water and oil. Lightly apply athin coating of anti-corrosion oil and let dry before storage.
7. Notes on storage:
Avoid direct sunlight, high temperatures, low temperatures, and highhumidity during storage.
If a digital height gage will not be used for more than three months, remove
the battery before storage.
If a protective cover is provided, use the cover during storage to prevent dust
from adhering to the column.

Fig. 1 conventional Instrumental error

JIS B 7517-1993
Specification range

This is not a very onerous specification. For example, the perpendicularity limit
allowable is 0.61 mm when L is 600 mm. This is because this error factor has
a small influence and does not change the inclination of the slider, unlike awarped column.
5. Relationship between accuracy and temperature
Height gages are made of several materials. Note that some combinations ofworkpiece material, room temperature, and workpiece temperature may affectmeasuring accuracy if this effect is not allowed for by performing a correction
calculation.
6. The tip of a height gage scriber is very sharp and must be handled carefully
if personal injury is to be avoided.
7. Do not damage a digital height gage scale by engraving an identification
number or other information on it with an electric marker pen.
8. Carefully handle a height gage so as not to drop it or bump it against
anything.

Non-conformity range

The height measurement error in a height gage is the indication error when
the reference edge (column) is perpendicular to the base reference surface
and the direction of contact is downward. Table 1 shows the maximum
permissible height measurement error E MPE.
E MPE for any desired height is obtained by measuring a gauge block, or
equivalent, with a height gage on a precision surface plate (Fig. 3) and thensubtracting the gauge block size from the measured size.
Table 1: M aximum permissible height measurement error E MPE of aconventional height gage
Measurement height
50 or lessOver 50, 100 or lessOver 100, 200 or lessOver 200, 300 or lessOver 300, 400 or lessOver 400, 500 or lessOver 500, 600 or lessOver 600, 700 or lessOver 700, 800 or lessOver 800, 900 or lessOver 900, 1000 or less

Unit: mm
Scale interval, graduation or resolution
0.05
0.02 or 0.01
±0.05
±0.02
±0.06
±0.03
±0.07
±0.08
±0.04
±0.09
±0.10
±0.05
±0.11
±0.12
±0.06
±0.13
±0.14
±0.07
±0.15

Note: E MPE includes the measurement error arising from straightness, flatness of the measuring
surface and parallelism with the reference surface.

Fig. 3: Determination of height measurement error

Acceptance range

4. Error due to inclination of the main scale (column)
According to JIS standards, the perpendicularity of the column reference edge
to the base reference surface should be better than:( 0 . 0 1 + 1000L ) mm L indicates the measuring length (unit: mm)

Conformity range

Non-conformity range

Maximum Permissible Error of heightmeasurement E MPE [JIS B 7517: 2018]

Uncertainty is not included in judgment
Specification range ＝Acceptance range

Gauge block
Height gage

New JIS Maximum Permissible Error (MPE)
JIS B 7517: 2018 (ISO/TR 14253-6: 2012)

Fig. 2

Non-conformity range(Rejected )UU

Uncertainty
rangeSpecification range
Conformity range
AcceptanceU

Non-conformity range(Rejected )U

Uncertainty
range

When a condition considering uncertainty is satisfied
Specification range ＝Conformity range

Precision surface plate

The “Instrumental error” indicating the indication error of JIS has been changed
to “Maximum Permissible Error (MPE) of indication” for the following models:• 192 Series Digimatic Height Gage described on page D-43 (All models)• 570 Series ABSOLUTE Digimatic Height Gage described on page D-45
(All models)• 570 Series Digimatic Height Gage described on page D-47 (All models)• 514, 506 Series Standard Height Gage with Adjustable Main Scaledescribed on page D-49 (All models)• 192 Series With digital counter described on page D-50 (All models)

Quick Guide to Measurement

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27

Depth Gages

Gauge Blocks

PG
28

JIS B 7518 was revised and issued in 2018 as the Japanese Industrial Standardsof the depth gage, and the “Instrumental error” indicating the indication errorof the depth gage has been changed to “Maximum Permissible Error (MPE) of
indication”.
The “Instrumental error” of the conventional JIS adopts acceptance criteriathat the specification range (precision specification) equals acceptance range,
and the OK/ NG judgment does not include measurement uncertainty (Fig. 1).
The “Maximum Permissible Error (MPE) of indication” of the new JIS employs
the basic concept of the OK / NG judgment taking into account the uncertainty
adopted in the ISO standard (ISO 14253-1).
The verification of conformity and nonconformity to the specifications isclearly stipulated to use the internationally recognized acceptance criteria(simple acceptance) when the specification range equals the acceptance
range, and it is accepted that the specification range equals the acceptance
range if a given condition considering uncertainty is met.
The above said internationally recognized acceptance criterion is ISO/TR
14253-6: 2012 (Fig. 2).
The following describes the standard inspection method including the revised
content of JIS 2018.

Fig. 1 conventional Instrumental error

JIS B 7518-1993
Conformity range

The Maximum Permissible Error E MPE of a depth gage is an indication error
applied to depth measurement.
Table 1 shows the Maximum Permissible Error E MPE of the indication value ofthe partial measuring surface contact error.
E MPE for any desired height is obtained by measuring the height of two equal
length gauge blocks, or equivalent, with a height gage on a precision surface
plate (Fig. 3) and then subtracting the gauge block size from the measured
size.
Table 1: Maximum permissible error E MPE of partial measuring face contact
of a conventional depth gage
Unit: mm
Scale interval, graduation or resolution
Measurement depth
0.05
0.02 or 0.01
50 or less
±0.05
±0.02
Over 50, 100 or less
±0.06
±0.03
Over 100, 200 or less
±0.07
Over 200, 300 or less
±0.08
±0.04
Over 300, 400 or less
±0.09
Over 400, 500 or less
±0.10
±0.05
Over 500, 600 or less
±0.11

Non-conformity range

Fig. 3: Determination of partial measuring face contact

Depth gage

Acceptance range

Gauge block

Uncertainty is not included in judgment
Specification range＝Acceptance range Height gage
Fig. 2New JIS Maximum Permissible Error (MPE)
JIS B 7518: 2018 (ISO/ TR 14253-6: 2012)

Non-conformity range(Rejected)
U

U

Specification range
Conformity range
Acceptance

Uncertainty
range

Gauge blockU

Definition of the Meter
The 17th General Conference of Weights and Measures in 1983
decided on a new definition of the meter unit as the length of the pathtraveled by light in a vacuum during a time interval of 1/299 792 458
of a second. The gauge block is the practical realization of this unit andas such is used widely throughout industry.

Selection, Preparation and Assembly of a Gauge Block Stack
Select gauge blocks to be combined to make up the size required forthe stack.
(1) Take the following things into account when selecting gauge blocks.
a. Use the minimum number of blocks whenever possible.
b. Select thick gauge blocks whenever possible.
c. Select the size from the one that has the least significant digit
		 required, and then work back through the more significant digits.
(2) Clean the gauge blocks with an appropriate cleaning agent.
(3) Check the measuring faces for burrs by using an optical flat asfollows:
Figure 1

Non-conformity range
Precision surface plate(Rejected)

Precision surface plate

When a condition considering uncertainty is satisfied
Specification range＝Conformity range

a. Wringing thickgauge blocks

b.Wringing a thick gauge
block to a thin gauge block

Cross the gauge blocks at 90˚in the middle of the measuring
faces.

Overlap one side of a thingauge block on one side of a
thick gauge block.

To prevent thin gauge blocks frombending, first wring a thin gauge
block onto a thick gauge block.

Rotate the gauge blocks
while applying slight force tothem. You will get a sense ofwringing by sliding the blocks.

Slide the thin gauge block
while pressing the entire
overlapped area to align themeasuring faces with eachother.

Then, wring the other thingauge block onto the first thingauge block.

Finally, remove the thickgauge block from the stack.

a. Wipe each measuring face clean.
b. Gently place the optical flat on the gauge block measuring face.
c. Lightly slide the optical flat until interference fringes appear.
Judgment 1: If no interference fringes appear, it is assumed that there		
is a large burr or contaminant on the measuring face.
d.Lightly press the optical flat to check that the interference
fringesdisappear.
Judgment 2: If the interference fringes disappear, no burr exists on		the measuring face.
Judgment 3: If some interference fringes remain locally while the flat		is gently moved to and fro, a burr exists on the		measuring face. If the fringes move along with the		optical flat, there is a burr on the optical flat.
e.Remove burrs, refer to the figures below for procedures.
Figure 3

c.Wringing thin gauge
blocksApply an optical flat to the surface
of one thin gauge block to check thewringing state.

Irregularinterference
fringesWipe the exposed measuring face(s) and continuebuilding up the stack, in the same manner as
above, until complete.

Figure 4

Thermal Stabilization TimeThe “Instrumental error” indicating the indication error of JIS has been changed
to “Maximum Permissible Error (MPE) of indication” for the following models:• 571 Series ABSOLUTE Digimatic Depth Gage described on page D-64
(All models)• 527 Series Vernier Depth Gage described on page D-65 (All models)• 527, 571 Series Hook End Type described on page D-66 (All models)• 571 Series Mini Depth Gage described on page D-67 (All models)RubberRubber
1 1
CERASTONCERASTON(Or(OrArkansas
Arkansasstone*
stone*) )The following figure shows the degree of dimensional change whenhandling a 100 mm steel gauge block with bare hands.

1 1
CERASTONCERASTON(Or(OrArkansas
Arkansasstone*
stone*) )(1) Wipe any dust and oil films from the gauge block and the Ceraston(or Arkansas stone) using a solvent.
(2) Place the gauge block on the Ceraston so that the measuring face thathas burrs is on the abrasive surface of the stone. While applying lightpressure, move the gauge block to and fro about ten times (Fig. 3).
Use a block rubber for thin gauge blocks to apply even pressure (Fig. 4).
(3) Check the measuring face for burrs with an optical flat. If the burrs
have not been removed, repeat step (2). If burrs are too large, they
may not be removed with an abrasive stone. If so, discard the gauge
block.
*1 Mitutoyo does not offer Arkansas stones.

PG

29

Align the measuring faces witheach other.

U

Uncertainty
range(5) Gently overlay the faces of the gauge blocks to be wrung together.
There are three methods to use (a, b and c as shown below)
according to the size of blocks being wrung:

Figure 2

Note: E MPE includes the measurement error arising from straightness, flatness of the measuring
surface and parallelism with the reference surface.

Specification range
Non-conformity range

Maximum Permissible Error of depth
measurement E MPE [JIS B 7518: 2018]

Elongation (µm)

Depth Gage Performance Evaluation Method

Time fingers are released

9
8
7
6
5
4
3
2
1

The gauge block is held with five fingers.

The gauge block is held with three fingers.

5 10

20

30

40

50

60

70

Lapse of time (minutes)(4) Apply a very small amount of oil to the measuring face and spreadit evenly across the face. (Wipe the face until the oil film is almost
removed.) Grease, spindle oil, vaseline, etc., are commonly used.
Quick Guide to Measurement

Dial Indicators, Digital Indicators and Test Indicators
Measuring orientation

Nomenclature

Position

Remarks

Cap

PG
30

PG

2
3

Vertical position(contact point downward)

1 0 9
4 5 6

31

8
7

—

Pointer (or hand)
Bezel

GroundRevolution counter
Graduations
Dial face

Lateral position(spindle horizontal)
GroundGroundIf measurement is performed in the lateral orientation, or upside-downorientation, the measuring force is less than in the vertical orientation. In this casebe sure to check the operation and repeatability of the indicator.
For guaranteed-operation specifications according to the operating orientationrefer to the specific product descriptions in the catalog.

Stem

4 5 6

8
7

Contact point

1 0 9

Upside-down position(contact point upward)

2
3

Spindle (or Plunger)

GroundMounting a Dial gage

MethodClamping the stem directlywith a screw

Clamping the stemby split-clamp fastening

ore

Setting the origin of a digital indicator

The accuracy specification in the range of 0.2 mm from the end of the stroke is not guaranteed for Digimatic indicators. When setting the zero point or presetting a
specific value, be sure to lift the spindle at least 0.2 mm from the end of the stroke.

rm
mo

8m

Stem
mounting

Note• Mounting hole tolerance: ø8G7 (+0.005 to 0.02)• Clamping screw: M4 to M6• Clamping position: 8 mm or more from the lower edge of the stem
• Mounting hole tolerance: ø8G7 (+0.005 to 0.02)• Maximum clamping torque: 150 N·cm when clamping with a single M5 screw• Note that excessive clamping torque may adversely affect spindle movement.
M6 screw
Plain washer

Method
0.2 mmLug mounting

Note• Lugs can be changed 90° in orientation according to the application. (The lug is set horizontally when shipped.)• Lugs of some Series 1 models (No.1911A-10, 1913A-10 and 1003A), however, cannot be altered to horizontal.
• To avoid cosine-effect error, ensure that any type of gage or indicator is mounted with its spindle in line with the intended measurement direction.

Care of the spindle
Contact point• Screw thread is standardized on M2.5 x 0.45 (Length: 5 mm).
• Incomplete thread section at the root of the screw shall be less than 0.7 mm
when fabricating a contact point.

spindle5

M2.5 × 0.45
Incomplete thread section
shall be less than 0.7 mm• Do not lubricate the spindle. Doing so might cause dust to accumulate, resulting in a malfunction.
• If the spindle movement is poor, wipe the upper and lower spindle surfaces with a dry or alcohol-soaked cloth. If the movement is not improved by cleaning, contact
Mitutoyo for repair.
• Before making a measurement or calibration, confirm if the spindle moves upward and downward smoothly, and stability of the zero point.

M2.5 × 0.45, depth 7 mm
ø3 counterbore, depth 1 mm

Quick Guide to Measurement

Dial Indicators, Digital Indicators and Test Indicators
Lever-operated dial indicator Standard B7533 : 2015 (Extract from JIS/Japanese Industrial Standards)

Dial Indicator Standard B7503 : 2017 (Extract from JIS/Japanese Industrial Standards)
Item

Indication error
over the entire One-revolution
measuring range dial indicator andmulti-revolution
1/10 revolution dial indicator
indication error

Evaluation method(performance evaluation by moving the zero point)
Obtain the difference between the maximum and theminimum values of indication error of all measurement
points in both retract and extend directions.
During the first two revolutions in both retract and extend
directions, obtain the maximum difference of the indication error
among the adjacent measurement points per 1/10 revolutions*3.
During the first five revolutions in both retract and extend directions,obtain the maximum difference of the maximum and the minimum
indication errors over the measuring range per 1/2 revolutions.
During the first ten revolutions in both retract and extend directions,obtain the maximum difference of the maximum and the minimum
indication errors over the measuring range per one revolution.

Set the dial indicator on the supporting stand,and read the indication error*1 of the next
point while gradually retracting the spindle.
- Every 1/10 revolution for the first two
revolutions*2
Indication- Every half revolution from two to fiveerror
revolutions
1/2 revolution- Every revolution from five to ten revolutions
indication error
Multi-revolution - Every five revolutions from 10 to 50
revolutions
dial indicator
1 revolution- Every ten revolutions after 50 revolutions
indication error
Next, after retracting the spindle for morethan three graduations of the long hand,
One-revolution extend the spindle gradually and read the Obtain the maximum difference of all the measuring points
dial
indicator
andindication error at the same measurement in reference to the indication error at the same measuring
Retrace error
multi-revolution point in the retract direction.
point in both forward and backward directions.
dial indicator

Measurement examples

Dial indicator

Supporting standMicrometer head or otherlength measuring unit

Dial indicator

Set the dial indicator on the supporting
stand, retract the spindle at a desired Obtain the maximum difference among five indication
position within the measuring range.
Then, extend the spindle quickly and values.
slowly five times and read each value.

Repeatability

One-revolution
dial indicator andmulti-revolution
dial indicator
Measuring force

No.

Item.
Measuring method
Indication error Holding the dial test indicator (lever type),
over the entire define the reference point at near the contact
1 measuring range point resting point where the indication and(in the forward error of indication is set zero.
direction)
Then, move the contact point in the forward
2

10 graduations
indication error

3

1 revolution
indication error

4 Retrace error

Supporting stand(Gauge block)
Measuring stage

5 Repeatability
Dial indicator

Measuring point

Evaluation method

DiagramObtain the difference between the maximum
and the minimum values of indication error of all
measurement points in the forward direction.

In the forward direction from the reference point
direction and read the error of indication at
Per 10to the end point, obtain the maximum differenceeach measuring point.
graduationsof the indication error among the adjacent
Next, after moving the contact point for morein the forward
measurement points per 10 graduations.
than three graduations from the end of theand backward
measuring range, move the contact point inIn the forward direction from the reference point
direction from thethe backward direction and read the error ofto the end point, obtain the maximum difference
reference point toindication at the same measurement point inof the maximum and the minimum indication
the end point.
the forward direction.
errors to be read by the zero-point fixed method(The forward direction is the direction against
over the measuring range per 1 revolution.
the measuring force to the contact point of
Obtain the maximum difference in reference tothe lever-operated dial indicator; the backward
the indication error at the same measuring point
direction is the measuring force appliedin both forward and backward directions among
direction.)
all the measurement points.

Lever-operated dial indicator

Supporting
stand

Micrometer head or
length measuring unit

Lever-operated dial indicator

Holding the dial test indicator (lever type)with its stylus parallel with the top face ofAt arbitrary
Obtain the maximum difference of the fivethe measuring stage, move the contact
points within themeasured values.
point quickly and slowly five times at ameasuring range
desired position within the measuring range
and read the indication at each point.

Supporting
stand

Supporting standSet the dial indicator on the supporting
stand, retract and extend the spindle
continuously and gradually, and readthe measuring force at the zero and end
points.

Obtain the maximum measuring force, the minimum
measuring force, and the difference of the measuringforce in both retract and extend directions at the samemeasurement point.

Top pan type spring
scale or force gage

Holding the dial test indicator (lever type),
move the contact point in the forward
6 Measuring force and backward directions continuously andgradually, and read the measuring force inthe measuring range.

Reference point
Obtain the maximum and the minimum values
and end point
in reference to the measuring force.
within themeasuring range

Lever-operated dial indicator

Top pan type spring scale*1: For how to read the indication error, either read the input quantity of the measuring instrument aligning the long hand to the graduation, or read the indication value of the dial
indicator according to the moving amount of the measuring instrument.					*2: With the one-revolution dial indicator, read the indication error per 10 graduations.					*3: With the one-revolution dial indicator, obtain the maximum difference of the indication error in the interval of adjacent 10 graduations.

Maximum permissible error
Maximum permissible error (MPE) by measurement
characteristics --dial indicators with bezel dia. 50 mm or
smaller and Back Plunger type dial indicators
Graduation (mm)
0.01
0.005
0.001
0.01
0.005 0.002 0.001
Over 1 Over 3 Over 5 Over 10 Over 20 Over 30 Over 50
Over 1 Over 2
Over 1 Over 3 Over 5
Measuring range 1 or less andup and up and up and up and up and up and up 5 or less 1 or less and up and up 1 or less and up and up and up 5 or less 1 or less 1 or less(mm)
to 5 to 10 to 20 to 30 to 50 to 100
to 5
to 5 to 10
to 3
to 2
to 3
Retrace error
3
3
3
3
5
7
8
9
3
2
2
3
4
4
4
5
3.5
2.5
2
Repeatability
3
3
3
3
4
5
5
5
3
0.5
0.5
1
3
3
3
3
3
1
1
Arbitrary 1/10
5
5
5
5
8
10
10
12
5
2
2
3.5
8
8
8
9
6
2.5
2.5
revolution
Arbitrary 1/2
8
8
9
9
10
12
12
17
9
3.5
4
5
11
11
12
12
9
4.5
4
revolution
Arbitrary One
8
9
10
10
15
15
15
20
10
4
5
6
12
12
14
14
10
5
4.5
revolution
Entiremeasuring
8
10
12
15
25
30
40
50
12
5
7
10
15
16
18
20
12
6
5
range
Note 1: The maximum permissible error (MPE) for one-revolution dial indicators does not specify the indication error of an arbitrary 1/2 and 1 revolution.
Note 2: The MPE represents the value at 20 ºC, which JIS B 0680 defines as the standard temperature.
Note 3: The measurement characteristics of a dial indicator have to meet both maximum permissible error (MPE) and measurement force permissible limits (MPL) at any position within themeasuring range in any posture when the measurement characteristics are not specified by the manufacturer.
Maximum permissible error (MPE) by measurement characteristics-- dial indicators with bezel dia. 50 mm or larger

Indication error

PG
32

Measuring method(zero-point fixed)

Model● Maximum permissible error and permissible limits
Graduation (mm)
Revolution

1 revolution

Measuring range (mm)0.3 or less

Measuring range (μm)
Error of indication over One revolution (μm)
a range of
10 scale divisions (μm)
Retrace error (µm)
Repeatability (µm)
Max.
Measuring force (N)
Min.

4
—
2
3
1
0.5
0.01

0.001/0.002
Multi-revolution
Over 0.3,
Over 0.5,
up to 0.5
up to 0.6
6
7
5
5
2
2
4
4
1
1
0.5
0.5
0.01
0.01

0.5 or less
6
—
5
4
3
0.5
0.01

0.01
1 revolution
Over 0.5, up to 1.0
L1 ≤ 35
35 < L1
9
10
—
—
5
5
4
5
3
3
0.5
0.5
0.01
0.01

Multi-revolution
Over 1.0,
up to 1.6
16
10
5
5
3
0.5
0.01

Mitutoyo's Response to Dial Indicator Standard B 7503 : 2017
• We guarantee the accuracy of completed products by inspecting them in the vertical posture. Standard-attached inspection certificate includes inspection data.
• We issue paid-for inspection certificates for horizontal or opposite posture if required.
• It is said that, for evaluation of the compatibility to the specifications, JIS B 0641-1 or the criteria where the internationally-recognized specification range and the
OK range are equal shall be applied. Also, it is said that the uncertainty is preferred to be evaluated based on ISO 14253-2 and ISO / IEC Guide 98-3. Therefore, we
perform shipping inspection of dial indicators inclusive of the uncertainty of calibration as in the past.

Quick Guide to Measurement

PG

33

Dial Indicators, Digital Indicators and Test Indicators

Linear Gages

Dial Test Indicators and the Cosine Effect

Head

PG
34

Workpiece movement direction
Stylus movement
direction

Workpiece movement direction
Stylus movement
direction

θ

L2

θ

L1

Always minimize the angle between movement directions during use.

L1: Result of
measurement
L2: Indicated value
L1=L2×Cos

Plain Stem and Stem with Clamp Nut

Precautions in Mounting LGH Series

The stem used to mount a linear gage head is classified as a "plain type" or"clamp nut type" as illustrated below. The clamp nut stem allows fast andsecure clamping of the linear gage head. The plain stem has the advantage ofwider application and slight positional adjustment in the axial direction on final
installation, although it does requires a split-fixture clamping arrangement oradhesive fixing. However, take care so as not to exert excessive force on thestem.

To fix the Laser Hologage, insert the stem into the dedicated stand or fixture.
Stem

Clamp

ストレートステム
Plain stem

Measuring ForceThis is the force exerted on a workpiece during measurement by the contact
point of a linear gage head, at its stroke end, expressed in newtons.
θComparative Measurement
A measurement method where a workpiece dimension is found by measuring
the difference in size between the workpiece and a master gage representing
the nominal workpiece dimension.

Clamp• Machine the clamping hole so that its axis is parallel with the measuring
direction. Mounting the gage at an angle will cause a measuring error.
• When fixing the Laser Hologage, do not clamp the stem too tightly. Overtightening the stem may impair the sliding ability of the spindle.
• If measurement is performed while moving the LGH Series, mount it so thatthe cable will not be strained and no undue force will be exerted on thegage head.

Display Unit
Zero-setting
The display value can be set to 0 (zero) at any position of the spindle.

Ingress Protection Codeθ

IP54 protection code
θ

Type
Level
Description
Protects the human body and 5: Dust protected Protection against harmful dust
protects against foreign objects
Protects against exposure to 4 : Splash-proof Water splashing against the enclosure from
water
type
any direction shall have no harmful effect.

IP66 protection code
The reading of any indicator will not represent an accurate measurement if its measuring direction is misaligned with the intended direction of
measurement (cosine effect). Because the measuring direction of a dial test indicator is at right angles to a line drawn through the contact point andthe stylus pivot, this effect can be minimized by setting the stylus to minimize angle (as shown in the figures). If necessary, the dial reading can becompensated for the actual value by using the table below to give the result of measurement.
Result of measurement = indicated value x compensation valueCompensating for a non-zero angle
Angle

Compensation value

10°

0.98

20°

0.94

30°

0.87

40°

0.77

50°

0.64

60°

0.50

ExamplesIf a 0.002 mm measurement is indicated on the dial atvarious values of , the result of measurements are:
For = 10˚, 0.002 mm×0.98=0.00196 mm
For = 20˚, 0.002 mm×0.94=0.00188 mm
For = 30˚, 0.002 mm×0.87=0.00174 mm

Mitutoyo's Response to Lever-operated Dial Indicator B 7533 : 2015
• In the finished product inspection, the accuracy is guaranteed using the horizontal, tilted, vertical type dial indicator with its dial face facing upward; the parallel typewith its dial face set in the vertical orientation.
Standard-attached inspection certificate includes inspection data.
• The inspection certificate for other than the above postures is available for a fee.
• It is said that, for evaluation of the compatibility to the specifications, the criteria based on JIS B 0641-1 or ISO/TR14253-6 shall be applied.
Also, it is said that the uncertainty is preferred to be evaluated based on ISO 14253-2 and ISO/IEC Guide 98-3. Therefore, we perform shipping inspection of dial
indicators inclusive of the uncertainty of calibration as in the past.
• For universal and pocket types, we perform the finished product inspection based on JIS B 7533-1990.

PG

35

Clamp screw

Recommended hole diameter on the fixing side: 15 mm +0.034/-0.014

ナット付ステム
Stemlocknut typeθ

Stem Clamp screw

Type
Level
Description
Protection against contact with the 6: Dust tightProtection from dust ingresshuman body and foreign objects
Complete protection against contact
Protects against exposure to 6 : Water-resistant Water jets directed against the enclosure from
water
type
any direction shall have no harmful effects.

0.000

0.000

0.000

Presetting
Any numeric value can be set on the display unit for starting the count fromthis value.

123.456

1.234

Direction changeover
Precautions in Mounting a Gage Head
• Insert the stem of the gage into the mounting clamp of a measuring unit ora stand and tighten the clamp screw.
• Notice that excessively tightening the stem can cause problems with spindle
operation.
• Never use a mounting method in which the stem is clamped by directcontact with a screw.
• Never mount a linear gage by any part other than the stem.
• Mount the gage head so that it is in line with the intended direction of
measurement. Mounting the head at an angle to this direction will cause anerror in measurement.
• Exercise care so as not to exert a force on the gage through the cable.

The measuring direction of the gage spindle can be set to either plus (+) or
minus (-) of count.
＋/−

Datum plane

MAX, MIN, TIR Settings
The display unit can hold the maximum (MAX) and minimum (MIN) values, andthe run out value (TIR) during measurement.

Runout value (TIR) = MAX - MIN

MAX

MIN

Quick Guide to Measurement

Linear Gages

PG
36

Tolerance Setting

BCD Output

Tolerance limits can be set in various display units for automatically indicating if
a measurement falls within those limits.

A system for outputting data in binary-coded decimal notation.

RS-232C Output
Open-collector Output
An external load, such as a relay or a logic circuit, can be driven from thecollector output of an internal transistor which is itself controlled by a Tolerance
Judgement result, etc.

A serial communication interface in which data can be transmitted bidirectionally under the EIA Standards.
For the transmission procedure, refer to the specifications of each measuring
instrument.

RS Link Function Multi-point measurement can be performed by connecting multiple EH counters with RS Link cables.
RS Link for EH Counter
It is possible to connect a maximum of 10 counter units and handle up to 20 channels of multi-point measurement at a time.
For this connection use a dedicated RS Link cable No.02ADD950 (0.5m), No.936937 (1m) or No.965014 (2m).
(The total length of RS Link cables permitted for the entire system is up to 10m.)

OUT

RS-232C connector

Digimatic Code
A communication protocol for connecting the output of measuring tools withvarious Mitutoyo data processing units. This allows output connection to a
Digimatic Mini Processor DP-1VA LOGGER for performing various statistical
calculations and creating histograms, etc.

Last counterFirst counter
IN

PG

37

IN

OUT

RS-232C connector

IN

OUT

RS-232C connector

RS-232C cable *Personal computer*Only the Mitutoyo software“SENSORPAK” can be used
when a USB cable is connected.
Gage number

01

02

03

04……

Quick
Quick Guide
Guide to Measurement

Linear Gages

Electronic Micrometers

Measurement Examples

Probe

Comparative measurement

A sensor that converts movement of a contact point, on a stylus or plunger,
into an electrical signal.

A measurement method where a workpiece dimension is found by measuring
the difference in size between the workpiece and a master gage that represents
the nominal dimension.
This method is usually applied when the measurement to be made is greaterthan the measuring range of the instrument.

Roll gap measurement

Chip parallelism measurement

PG
38

Lever probes
Lever probes are available in two types. The most common type uses a pivoted
stylus so the contact point moves in a circular arc; this type is subject to cosine
effect and, therefore, measurements may require linearity correction if thedirection of measurement is much different to the direction of movementof the contact point. The less common type uses a parallel translation leafspring mechanism so contact point movement is linear; this type requires nocorrection.

Linearity
The ratio of proportionality between measuring system output and measured
distance.
If this is not constant within acceptable limits then correction is required.

0 (zero) point
A reference point on the master gage in a comparative measurement.

Pivoted stylus type

FPD board multipoint measurement

MLH-521 (measuring direction can be switchedwith the up/down lever)
MLH-522 (measuring direction is not switchable)

Cam-lift measurement

Sensitivity
The ratio of the electric micrometer output signal to the input signal to theamplifier. The sensitivity is normal if a value as expected from the given
displacement is displayed.

Parallel translation typeMLH-326 (measuring direction can be switchedwith the upper dial)

Tolerance setting
Tolerance limits can be set on the electronic micrometer to provide anautomatic judgment as to whether a measured value falls within the tolerance.

Pre-travel
The distance from first contact with a workpiece until the measurement
indicator reads zero.
0

Brake disk multipoint measurement

Lever-head angle
Before measurement, be sure to confirm that probe sensitivity adjustment has
been completed.
Changing the probe angle will cause variation in the measured values. Adjust
the probe angle to obtain an optimum sensitivity before starting measurement.
If it is difficult, adjust the sensitivity with the probe angle set to 0°, and after
measurement, correct the measured values according to the actual probe angle(by multiplying the measured value by a correction factor).

0

Machine device tool length measurement

Tips Correction using a correction factor may result in lower accuracy
than when adjusting sensitivity with the actual probe angle.

First contact.
moves until the
測定子を測定子が Plunger
indicator
reads zero.
メータがフリーの状態
0になるまでゼロ

Measuring force
Workpiece discrimination

Inspection fixture

The force applied to the workpiece by the probe when the indicator registers
zero. It is indicated in newtons (N).

Digimatic code
A communication protocol for connecting the output of measuring tools withvarious Mitutoyo data processing units. This allows output connection to a
Digimatic Mini Processor DP-1VA LOGGER for performing various statistical
calculations and creating histograms, etc.

Open collector output
A direct connection to the collector of a driving transistor.

+90°
0°
-90°

Angle: θ

Bottom surface of theprobe
L

押込んだ状態

Workpiece surface

Angle: θ
0°
10°
20°
30°
40°
50°
60°

Distance from the workpiecesurface: L*―
Approx. 3.1 mm
Approx. 8.8 mm
Approx. 13.9 mm
Approx. 18.3 mm
Approx. 21.6 mm
Approx. 23.8 mm

Correction factor
1.00
Approx. 0.98
Approx. 0.94
Approx. 0.87
Approx. 0.77
Approx. 0.64
Approx. 0.50

* Value when using a carbide probe with spherical diameter of ø2 that is installed
before shipment. When using a ø1 (or ø3) carbide probe, subtract (or add) 1/2 ofthe difference in spherical diameter.

Quick Guide to Measurement

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39

Laser Scan Micrometers

PG
40

Compatibility

Re-assembly after removal from the baseYour Laser Scan Micrometer has been adjusted together with the ID Unit, which
is supplied with the measuring unit. The ID Unit, which has the same code
number and the same serial number as the measuring unit, must be installedin the display unit. This means that if the ID Unit is replaced the measuring unit
can be connected to another corresponding display unit.

Observe the following limits when re-assembling the emission unit andreception unit to minimize measurement errors due tomisalignment of the laser's optical axis with the reception unit.

The workpiece and measuring conditions
Depending on whether the laser is visible or invisible, the workpiece shape,
and the surface roughness, measurement errors may result. If this is the case,perform calibration with a master workpiece which has dimensions, shape, andsurface roughness similar to the actual workpiece to be measured.
If measurement values show a large degree of dispersion due to the measuringconditions, increase the number of scans for averaging to improve themeasurement accuracy.

Measurement Examples
Measurement of outside diameter of rubber roll

Simultaneous measurement of roller outside diameter and deflection

PG

41

Alignment within the horizontal planea. Parallel deviation between reference lines C and D:
X (in the transverse direction)
Reference line D
Reference line C

X

b. Angle between reference lines C and D:θx (angle)
Reference line D

Electrical interference

Reference line C

To avoid operational errors, do not route the signal cable and relay cable of theLaser Scan Micrometer alongside a highvoltage line or other cable capable ofinducing noise current in nearby conductors. Ground all appropriate units andcable shields.

Measurement of uneven thickness of film or sheet (simultaneous measurement)

Measurement of gap between rollers

Measurement of film sheet thickness

Dual system for measuring a large outside diameterθx

Alignment within the vertical plane

Connection to a computerc. Parallel deviation between reference planes A and B: Y (in height)

If the Laser Scan Micrometer is to be connected to an external personal
computer via the RS-232C interface, ensure that the cable connections conformto the specification.

Laser safety
Mitutoyo Laser Scan Micrometers use a low-power visible laser formeasurement. The laser is a CLASS 2 EN/IEC60825-1 device. Warning andexplanation labels, as shown right, are attached to the Laser Scan Micrometers
as is appropriate.

Reference plane B
Reference plane AY

d. Angle between reference planes A and B:θy (angle)
Reference plane B
Reference plane AθyAllowable limits of optical axis misalignment
Model
LSM-501S
LSM-503S
LSM-506S
LSM-512S
LSM-516S

Distance between
Emission Unit
and Reception Unit

X and Yθx and θy

68 mm ( 2.68") or lesswithin 0.5 mm (.02")

within 0.4˚ (7 mrad)

100 mm ( 3.94") or lesswithin 0.5 mm (.02")

within 0.3˚ (5.2 mrad)

130 mm ( 5.12") or lesswithin 1 mm (.04")

within 0.4˚ (7 mrad)

350 mm (13.78") or lesswithin 1 mm (.04")

within 0.16˚ (2.8 mrad)

273 mm (10.75") or lesswithin 1 mm (.04")

within 0.2˚ (3.5 mrad)

700 mm (27.56") or lesswithin 1 mm (.04")

within 0.08˚ (1.4 mrad)

321 mm (12.64") or lesswithin 1 mm (.04")

within 0.18˚ (3.6 mrad)

700 mm (27.56") or lesswithin 1 mm (.04")

within 0.08˚ (1.4 mrad)

800 mm (31.50") or lesswithin 1 mm (.04")

within 0.09˚ (1.6 mrad)

Quick Guide to Measurement

Linear Scales
Glossary■ Absolute system

PG
42

A measurement mode in which every point measurement is maderelative to a fixed origin point.
■ Incremental system

A measurement mode in which every point measurement is maderelative to a certain stored reference point.
■ Origin offset

A function that enables the origin point of a coordinate system to betranslated to another point offset from the fixed origin point. For thisfunction to work, a system needs a permanently stored origin point.
■ Restoring the origin point

A function that stops each axis of a machine accurately in position
specific to the machine while slowing it with the aid of integrated limit
switches.
■ Sequence control

A type of control that sequentially performs control steps according
to a prescribed order.
■ Numerical control

A way of controlling the movements of a machine by encodedcommands created and implemented with the aid of a computer (CNC).
A sequence of commands typically forms a ‘part program’ that instructs
a machine to perform a complete operation on a workpiece.

Specifying Linear Scale Accuracy■ BCD

A notation of expressing the numerals 0 through 9 for each digitof a decimal number by means of four-bit binary sequence. Datatransmission is one-way output by means of TTL or open collector.
■ RS-422

An interface standard that uses serial transmission of bits in differential
form over a balanced transmission line. RS-422 is superior in its datatransmission characteristics and in its capability of operating with only asingle power supply of 5 VDC.

Positional Indication accuracy
The accuracy of a linear scale is determined by comparing the positional value indicated by the linear scale with the corresponding value from a laser
length measuring machine at regular intervals using the accuracy inspection system as shown in the figure below. As the temperature of the inspection
environment is 20 °C, the accuracy of the scale applies only in an environment at this temperature. Other inspection temperatures may be used tocomply with internal standards.
Computer
Laser length measuringmachine counter

Digital counter■ Accuracy

The accuracy specification of a scale is given in terms of the maximum
error to be expected between the indicated and true positions at any
point, within the range of that scale, at a temperature of 20ºC.
Since there is no international standard defined for scale units, eachmanufacturer has a specific way of specifying accuracy. The accuracy
specifications given in our catalog have been determined using laserinterferometry.

Optical axis of laser beam
Cube corner
Interferometer

FixtureLaser source

Scale unit

■ Narrow range accuracy

Scale gratings on a scale unit normally adopt 20µm pitch though it
varies according to the kind of scale. The narrow range accuracy refers
to the accuracy determined by measuring one pitch of each grating at
the limit of resolution (1µm for example).

Movable table■ Binary output

Refers to output of data in binary form (ones and zeros) that represent
numbers as integer powers of 2.
■ RS-232C

An interface standard that uses an asynchronous method of serialtransmission of data over an unbalanced transmission line for dataexchange between transmitters located relatively close to each other.
It is a means of communication mainly used for connecting a personal
computer with peripherals.

The accuracy of the scale at each point is defined in terms of an error value that is calculated using the following formula:
Error = Value indicated by Laser length measuring machine− Corresponding value indicated by the linear scale
A graph in which the error at each point in the effective positioning range is plotted is called an accuracy diagram.
There are two methods used to specify the accuracy of a scale, unbalanced or balanced, described below.

■ Line driver output

This output features fast operating speeds of several tens to several
hundreds of nanoseconds and a relatively long transmission distance ofseveral hundreds of meters. A differential-voltmeter line driver (RS422A
compatible) is used as an I/F to the NC controller in the linear scale
system.

(1) Unbalanced accuracy specification - maximum minus minimum error
This method simply specifies the maximum error minus the minimum
error from the accuracy graph, as shown below. It is of the form: E =( α +β L)µm. L is the effective range (mm), and α and β are factors
specified for each model.
For example, if a particular type of scale has an accuracy specification

Scale error at any point in range relative to start of range

0

3L
̶
̶
̶
of (3 + ̶1000 )µm and an effective range of 1000 mm, E is 6 µm.

(2) Balanced accuracy specification - plus and minus about the mean error
This method specifies the maximum error relative to the mean error
E (μm). This isfrom the accuracy graph. It is of the form: e = ±̶2
mainly used in separate-type (retrofit) scale unit specifications.

Maximum differencein scale error: E(µm)

Error

Error
0

Effective range

X Measuring point

Mean error
Effective range

Maximum error about
E (µm)
mean error: ±—2
X Measuring point

A linear scale detects displacement based on graduations of constant pitch. Two-phase sinusoidal signals with the same pitch as the graduations are
obtained by detecting the graduations. Interpolating these signals in the electrical circuit makes it possible to read a value smaller than the graduations
by generating pulse signals that correspond to the desired resolution. For example, if the graduation pitch is 20 µm, interpolated values can generate aresolution of 1 µm.
The accuracy of this processing is not error-free and is called interpolation accuracy. The linear scale's overall positional accuracy specification depends
both on the pitch error of the graduations and interpolation accuracy.

Quick Guide to Measurement

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43

Profile Projectors

Microscopes

Erect Image and Inverted ImageF

Projection screen

F

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44

An image of an object projected onto a screen is erect if it is orientatedthe same way as the object on the stage. If the image is reversed top
to bottom, left to right and by movement with respect to the object on
the stage (as shown in the figure below) it is referred to as an inverted
image (also known as a reversed image.)• Coaxial surface illumination: An illumination method whereby aworkpiece is illuminated by light transmitted coaxially to the lensfor the observation/measurement of the surface. (A half-mirror or a
projection lens with a built-in half-mirror is needed.)• Oblique surface illumination: A method of illumination by obliquely
illuminating the workpiece surface. This method provides animage of enhanced contrast, allowing it to be observed threedimensionally and clearly. However, note that an error is apt to occur
in dimensional measurement with this method of illumination.
(An oblique mirror is needed. Models in the PJ-H30 series aresupplied with an oblique mirror.)

Parallax error
An erect image

An inverted imageFF

Top of the stage

F Workpiece
X-axis movement
Y-axis movement

This is the displacement of an object against a fixed backgroundcaused by a change in the observer's position and a finite separationof the object and background planes. Can cause a reading error on a
projector screen.
Apparent position of object against screen
Object (e.g. a reading scale graduation line)

Working distance

Parallax error

Refers to the distance from the face of the projection lens to thesurface of a workpiece in focus. It is represented by L in the diagram
below.

Normal viewing position

Magnification Accuracy
The magnification accuracy of a projector when using a certain lens isestablished by projecting an image of a reference object and comparing
the size of the image of this object, as measured on the screen, withthe expected size (calculated from the lens magnification, as marked)
to produce a percentage magnification accuracy figure, as illustrated
below. The reference object is often in the form of a small, graduatedglass scale called a `stage micrometer’ or `standard scale’, and the
projected image of this is measured with a larger glass scale known asa `reading scale’.
(Note that magnification accuracy is not the same as measuring accuracy.)

L− M
ΔM(%) = ̶̶̶X 100
		M
ΔM(%): Magnification accuracy expressed as a percentageof the nominal lens magnification
L : Length of the projected image of the reference object
measured on the screen: Length of the reference object
M : Magnification of the projection lens

An optical system in which the image is formed by an objective and atube lens with an 'Infinity Space' between them, into which optical accessories can be inserted.
Objective lens
Image forming (tube) lensLight from point source is focusedat the intermediate image plane

A point-source on
the specimen

NA = n·Sinθ
The formula above shows that NA depends on n, the refractive index
of the medium that exists between the front of an objective and thespecimen (for air, n=1.0), and angle θ, which is the half-angle of the
maximum cone of light that can enter the lens.

Resolving Power (R)f1f2

Magnification of the objective = f2/f1

Infinity space

Finite-corrected Optical System

The minimum detectable distance between two image points,
representing the limit of resolution. Resolving power (R) is determinedby numerical aperture (NA) and wavelength (λ) of the illumination.
l
R=
(µm)
2·NA
            l = 0.55 μm is often used as the reference wavelength

Working Distance (W.D.)

Field of view diameter

Field of view diameter (mm) =Workpiece

The NA figure is important because it indicates the resolving powerof an objective lens. The larger the NA value the finer the detail thatcan be seen. A lens with a larger NA also collects more light and will
normally provide a brighter image with a narrower depth of focus than
one with a smaller NA value.

An optical system in which the image is formed only by an objective lens.
Objective lensA point-source on
the workpiece

L1

L2

Light from point source is focusedat the intermediate image plane

Magnification of the objective = L2/L1

Offset viewing position

Projector screen

The maximum diameter of workpiece that can be projected using aparticular lens.

Workpiece stage

Infinity Optical System

True position of
object against screen

Projection lensL

Numerical Aperture (NA)

Screen diameter of profile projector
Magnification of projection lens used

Example: If a 5X magnification lens is used for a projector with ascreen of ø500 mm:
Field of view diameter is given by 500 mm = 100 mm
5

The distance between the front end of a microscope objective and thesurface of the workpiece at which the sharpest focusing is obtained.

Parfocal Distance
Distance between the surface of the specimen and the objective's
seating surface when in focus.

Focal point on the image side

Projection screen surface

unit: mm

The distance from the principal point to the focal point of a lens: if
f1 represents the focal length of an objective and f2 represents the
focal length of an image forming (tube) lens then magnification isdetermined by the ratio between the two. (In the case of the infinitycorrection optical system.)
Focal length of the image-forming (tube) lensObjective magnification =		
Focal length of the objective
Example: 1X = 200
Example: 10X = 200
		 200		
20

Telecentric Optical System
An optical system based on the principle that the primary rays arealigned parallel to the optical axis by placing a lens stop on the focal
point on the image side. Its functional feature is that the image will notvary in size even though the image blurs as the object is shifted along
the optical axis.
For measuring projectors and measuring microscopes, an identical effectis obtained by placing a lamp filament at the focal point of a condenser
lens instead of a lens stop so that the object is illuminated with parallel
beams. (See the figure below.)

Focal Length (f)Working
distance
Parfocal distance

Focal Point

Working distanceLight rays traveling parallel to the optical axis of a converging lenssystem and passing through that system will converge (or focus) to apoint on the axis known as the rear focal point, or image focal point.
Parfocal distancePrincipal ray
Light source (lamp)
Optical axis

Type of Illumination• Contour illumination: An illumination method to observe a
workpiece by transmitted light and is used mainly for measuring themagnified contour image of a workpiece.

Condenser lensWorkpiece

Projection lensWorkpiece surface

Quick Guide to Measurement

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45

Microscopes
This is the distance (measured in the direction of the optical axis)
between the two planes which define the limits of acceptable
image sharpness when the microscope is focused on an object. As
the numerical aperture (NA) increases, the depth of focus becomesshallower, as shown by the expression below:
DOF = l 2 l = 0.55 μm is often used as the reference wavelength2·(NA)
Example: For an M Plan Apo 100X lens (NA = 0.7)
The depth of focus of this objective is0.55 μm = 0.6 μm
2 x 0.72

Bright-field and Dark-field Illumination
In bright-field illumination a full cone of light is focused by the objectiveon the specimen surface. This is the normal mode of viewing with an
optical microscope. With dark-field illumination, the inner area of thelight cone is blocked so that the surface is only illuminated by lightfrom an oblique angle. Dark-field illumination is good for detecting
surface scratches and contamination.

Apochromat and Achromat Objective
An apochromat objective is a lens corrected for chromatic aberration(color blur) in three colors (red, green, blue).
An achromat objective is a lens corrected for chromatic aberration in
two colors (red, blue).

Magnification
The ratio of the size of a magnified object image created by an
optical system to that of the object. Magnification commonly refers tolateral magnification although it can mean lateral, vertical, or angularmagnification.

Principal Ray

A ray considered to be emitted from an object point off the opticalaxis and passing through the center of an aperture diaphragm in a lenssystem.

Aperture Diaphragm
An adjustable circular aperture which controls the amount of light
passing through a lens system. It is also referred to as an aperture stopand its size affects image brightness and depth of focus.

Field Stop
An aperture which controls the field of view in an optical instrument.

Erect Image

Vision Measurement

An image in which the orientations of left, right, top, bottom andmoving directions are the same as those of a workpiece on theworkstage.

Vision measuring machines mainly provide the following processing capabilities.

Field number (FN), real field of view, andmonitor display magnification■ Edge detection

Detecting/measuring edges in the XY plane

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47

unit: mm

The observation range of the sample surface is determined by thediameter of the eyepiece’s field stop. The value of this diameter inmillimeters is called the field number (FN). In contrast, the real field ofview is the range on the workpiece surface when actually magnified
and observed with the objective lens.
The real field of view can be calculated with the following formula:■ Auto focusing

Focusing and Z measurement(1) The range of the workpiece that can be observed with themicroscope (diameter)
Real field of view =FN of eyepiece
Objective lens magnification

Example: The real field of view of a 10X lens is 2.4 =24
10

Alignment, positioning, and checking a feature(2) Monitor observation range
Monitor observation range = The size of the camera image sensor (diagonal length)
Objective lens magnification
Size of image sensor
Format1/ 3 in1/ 2 in
2/3 inDiagonal length
6.0
8.0
11.0

■ Pattern recognition

Length4.8
6.4
8.8

Image Storage
An image is comprised of a regular array of pixels. This is just like a picture on fine plotting paper with each square solid-filled differently.

Height3.6
4.8
6.6(3) Monitor display magnification
Monitor display magnification =640 pixels

Display
screenCCD
Video signal
cameralens

Display diagonal length on the monitor
Objective lens magnification x
Diagonal length of camera image sensor

PC

High-speed
A/D converter

Frame grabber

AmplifierGray Scale
A PC stores an image after internally converting it to numeric values. A numeric value is assigned to each pixel of an image. Image quality varies
depending on how many levels of gray scale are defined by the numeric values. The PC provides two types of gray scale: two-level and multi-level. The
pixels in an image are usually displayed as 256-level gray scale.
Display

2-level gray scale

screen scaleMulti-level gray
CCD
Video signal
cameralens

WhiteHigh-speed
A/D converter

Amplifier
White
1
1

PC
Frame grabber

255

255

White

White

Gray

Gray
127

127

Black

Black
0

0

640 pixels

Telecentric System
An optical system where the light rays are parallel to the opticalaxis in object and/or image space. This means that magnification isnearly constant over a range of working distances, therefore almost
eliminating perspective error.

Gray

Gray

Black

0
Black

Pixels in an image brighter than a given level are displayed as white and all other pixels
are displayed as black.

0

480 pixels

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46

unit: mm

480 pixels

Depth of Focus (DOF)

Vision Measuring Machines

Each pixel is displayed as one of 256 levels between black and white. This allows highfidelity images to be displayed.

Quick Guide to Measurement

Vision Measuring Machines
Edge Detection

Measurement along Multiple Portions of an Image

An image consists of pixels. If the number of pixels in a section to bemeasured is counted and is multiplied by the size of a pixel, then thesection can be converted to a numeric value in length. For example,
assume that the total number of pixels in the lateral size of a square
workpiece is 300 pixels as shown in the figure below.
If a pixel size is 10 μm under imaging magnification, the total length of
the workpiece is given by 10 μm x 300 pixels = 3000 μm = 3 mm.

How to actually detect a workpiece edge in an image is described using
the following monochrome picture as an example. Edge detection is
performed within a given domain. A symbol which visually defines
this domain is referred to as a tool. Multiple tools are provided to suitvarious workpiece geometries or measurement data.

Large features that cannot be contained on one screen have to bemeasured by precisely controlling the position of the sensor and stage
so as to locate each reference point within individual images. By thismeans the system can measure even a large circle, as shown below, bydetecting the edge while moving the stage across various parts of theperiphery.

The edge detection system scans within the tool area
as shown in the figure at left and detects the boundary
between light and shade.

Composite Coordinates of a Point
Since measurement is performed while individual measured positions are stored, the system can measure dimensions that cannot be included in one
screen, without problems.
Vision coordinate system

Gray scale

Machine coordinate system
255

M

127
0

Tool position
(1)

(2)

(1) Scan start position(2) Edge detection position(3) Scan end position

Mz

Vx
V

My

(3)

Vy

244

241

220

193

97

76

67

52

53

53

243

242

220

195

94

73

66

54

53

55

244

246

220

195

94

75

64

56

51

50

Example of numeric values assigned to pixels on the tool

High-resolution Measurement

Mx

Measuring machine stage position M = (Mx, My, Mz)

Detected edge position (from the center of vision) V = (Vx, Vy)

Actual coordinates are given by X = (Mx + Vx), Y = (My + Vy), andZ = Mz, respectively.

Principle of Auto Focusing

10 µm

300 pixels

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49

Tool

10 µm

300 pixels

The system can perform XY-plane measurement, but cannot performheight measurement using only the camera image. The system iscommonly provided with the Auto Focus (AF) mechanism for heightmeasurement. The following explains the AF mechanism that uses acommon image, although some systems may use an AF laser.

When enlarged...

Variation in Contrast Depending on the Focus
Condition
Edge contrast is low due toout-of-focus edges.
HighZ
coordinate

Gray scale

Gray scale

Edge contrast is high due
to sharp, in-focus edges.
High

Contrast

Tool position

A position the system recognizes as an edge may be in error by up to one
pixel width using normal image processing.
This will prevent the execution of high-resolution measurement.

Low
Contrast in the scanning direction

In-focusheightTool position

High

Low

CameraThe AF system analyzes an image while moving the Camera up and down in the Z axis.
In the analysis of image contrast, an image in sharp focus will show a peak contrast andone out of focus will show a low contrast. Therefore, the height at which the image
contrast peaks is the just-in-focus height.

High
Low

Low
Contrast in the scanning direction

Contrast in the scanning direction

Overview of ISO 10360-7

ISO10360-7 (Geometrical product specifications (GPS) -- Acceptance and reverification tests for coordinate measuring machines (CMM) -- Part 7: CMMs
equipped with imaging probing systems) was published on June 1, 2011.
Some inspecting items are listed in ISO10360-7. The following summarizes the test method for determining length measurement error (E) and probing error (PF2D).

Tool position

Gray scale

To increase the accuracy in edge detection, sub-pixel image processing is used.
An edge is detected by determining interpolation curve from adjacent pixel data as shown below.
As a result, it allows measurement with a resolution higher than 1 pixel.

Gray scale

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48

Dimensional Measurement

Length measurement error, EZ
coordinate

CCD
Five test lengths in seven different directions within the measuring
volume, eachlength measured three times, for a total of 105 measurements. Four directions are the
In-focus
space diagonals; remaining three positions are user specified; default locations
height areparallel to VMM axes.
When CTE (coefficient of thermal expansion) of the test-length artifact is < 2×10-6/K,
Contrast
additional measurement of artifact with normal CTE (8 to 13×10-6/K) is performed.

Tool position

Probing error, PF2D
Measure 25 points distributed evenly around the test circle (14.4º pitch).
Each of the 25 points shall be measured by using the specified 25 areas of the
field of view.
Calculate probing error as the range of the 25 radial distances (Rmax - Rmin)from the center of the least-square circle.

Field of view

Image signal without sub-pixel processing

Image signal with sub-pixel processing

The image signal profile approaches an analog
waveform like this.

4 positions(space diagonals)

3 positions(user specified)

Normal CTE
additional inspection

Quick Guide to Measurement

Contrast in

PG
50

ISO 4287: 1997 Geometrical Product Specifications (GPS) –Surface Texture: Profile method– Terms, definitions, and surface texture parameters
ISO 4288: 1996 Geometrical Product Specifications (GPS) –Surface Texture: Profile method– Rules and procedures for the assessment of surface texture
ISO 3274: 1996 Geometrical Product Specifications (GPS) –Surface Texture: Profile method– Nominal characteristics of contact (stylus) instruments
ISO 11562: 1996 Geometrical Product Specifications (GPS) –Surface Texture: Profile method– Metrological characteristics of phase-correct filters

Elements of Contact Type Surface Roughness Measuring Instruments

ISO 3274: 1996 (JIS B 0651: 2001)

Input/Output

Stylus tip

Surface

Amplifier

A profile filter is a phase-correct filter without phase delay (cause ofprofile distortion dependent on wavelength).
The weight function of a phase-correct filter shows a normal (Gaussian)
distribution in which the amplitude transmission is 50 % at the cutoff
wavelength.

Nominalform
removalTotal
profileAD
converter

Measurement
loop

Reference
guide skid

External
disturbancesFeeddeviceColumnDrive Unit

Feed device

ProfilefilterλS

Primary
profileAnalysisaccording to
ISO 4287

Surface profileon the real surface

Reference
profileISO 4287:1997 (JIS B 0601: 2013)
Primary profile

100
Roughness profile

PG

Waviness profile

51

50

λs

Data Processing Flow

TracedprofileTransducer

Surface Profiles

Input/Output

Z-axis Signal Transfer Unit

Probe

Metrological Characterization of Phase
Correct Filters
ISO 11562: 1996 (JIS B 0632: 2001)

Amplitude Transmission %Surftest (Surface Roughness Testers)

λc

λf

Wavelength

Definition: Profile that results fromthe intersection of the real surface
and a plane rectangular to it.

Primary Profile
Profile obtained from the measured profile by applying a low-pass filter
with cutoff valueλs.

Measurement
Traced profile

Definition: Locus of the centerof the stylus tip that traces theworkpiece surface
AD conversion

Measuring loop

Total profile

Probe (pickup)
Workpiece

Definition: Data obtained byquantizing the measured profile
Suppresses irrelevant geometry of the surface
such as inclination of a flat feature andcurvature of a cylindrical feature using theleast squares method.

StylusFixtureRoughness Profile
Profile obtained from the primary profile by suppressing the longer
wavelength components using a high-pass filter of cutoff valueλc.

Low-pass filterof cutoff value λs

BaseStatic Measuring Force (JISB0651)

Stylus Shape
A typical shape for a stylus end is conical with a spherical tip.
Tip radius: rtip = 2 µm, 5 µm or 10 µm
Cone angle: 60°, 90°
In typical surface roughness testers, the taper angle of the stylus
end is 60˚ unless otherwise specified.
60°

90°

Relationship between Cutoff Value and Stylus Tip Radius
The following table lists the relationship between the roughness profile
cutoff value lc, stylus tip radius rtip, and cutoff ratio lc/ls.

µ
R2

R2

λc

m

µm
60°

R5

R5

µm

µm
90°

λs

λc/ λsµm

Primary profile

Primary profile parameters

High-pass filterof cutoff valueλs

Band-pass filter that passes
wavelengths between cutoff
valuesλc andλf

Roughness profile

Waviness profile

Roughness
profile parameters

Waviness
profile parameters

Waviness Profile
Profile obtained by applying a band-pass filter to the primary profile toremove the longer wavelengths aboveλf and the shorter wavelengths
belowλc.

Maximum rtip

m

0µ

R1

m

0µ

R1

Maximum sampling length
µm
0.08
2.5
30
2
0.5
0.25
2.5
100
2
0.5
0.8
2.5
300
0.5
2 Note 1
2.5
8
300
1.5
5 Note 2
825300
10 Note 2
5
Note 1: F or a surface with Ra>0.5 µm or Rz>3 µm, a significant error will not usuallyoccur in a measurement even if rtip = 5 µm.
Note 2: If a cutoff value ls is 2.5 µm or 8 µm, attenuation of the signal due to themechanical filtering effect of a stylus with the recommended tip radiusappears outside the roughness profile pass band. Therefore, a small error instylus tip radius or shape does not affect parameter values calculated frommeasurements.
If a specific cutoff ratio is required, the ratio must be defined.

mm

90°

60°

Nominal radius of
Static measuring force atTolerance on static
curvature of stylus tip:
the mean position of
measuring forceµm
stylus: mNvariations: mN/µm
2
0.75
0.035
5
Note 10.2
0.75 (4.0)
10Note 1: The maximum value of static measuring force at the average position of a stylus
is to be 4.0 mN for a probe with a special structure including a replaceable stylus.

µm

Quick Guide to Measurement

Surftest (Surface Roughness Testers)

Evaluation lengthZplwith l as lp, lr, or lw according to the case.

Zv

Sampling length

In Old JIS and ISO 4287-1: 1984, Rz was used to indicate the“ten point height of irregularities”. Care must be taken
because differences between results obtained according to
the existing and old standards are not always negligibly small.
(Be sure to check whether the drawing instructions conformto existing or old standards.)

Root mean square deviation of the primary profile Pq
Root mean square deviation of the roughness profile Rq
Root mean square deviation of the waviness profile Wq
Root mean square value of the ordinate values Z(x) within a sampling
lengthPq, Rq, Wq =

Zp1
Zv4

Zp4
Zp5

(Zp1 + Zp2 + Zp3 + Zp4 + Zp5) + (Zv1 + Zv2 + Zv3 + Zv4 + Zv5)
5

i=1

Xs2

Xs3

Xs4

Xs5

Sampling length

Xs6
SymbolRzJIS82

Amplitude Parameters (average of ordinates)
Arithmetical mean deviation of the primary profile Pa
Arithmetical mean deviation of the roughness profile Ra
Arithmetical mean deviation of the waviness profile Wa
Arithmetic mean of the absolute ordinate values Z(x) within a sampling
lengthPa, Ra, Wa = 1 ∫|Z(x)|dx
l 0

RzJIS =

1 m
PSm, RSm, WSm = m ∑ XSi
Xs1

Maximum height of the primary profile Pz
Maximum height of the roughness profile Rz
Maximum height of the waviness profile Wz
Sum of height of the largest profile peak height Zp and the largest profile valley depth Zv within a sampling length

JIS Specific Parameters
Ten-point height of irregularities, RzJIS
Sum of the absolute mean height of the five highest profile peaks andthe absolute mean depth of the five deepest profile valleys, measured
from the mean line within the sampling length of a roughness profile.
This profile is obtained from the primary profile using a phase-correct
band-pass filter with cutoff values of lc and ls.

Zp2

Spacing Parameters
Mean width of the primary profile elements PSm
Mean width of the roughness profile elements RSm
Mean width of the waviness profile elements WSm
Mean value of the profile element widths Xs within a sampling lengthdZ (x)
dx

Zv1

Rz
Rz

Rt

Rv
Sampling length

The above equation defines Rku. Pku and Wku are defined in a similarmanner. Pku, Rku, and Wku are measures of the sharpness of the probability density function of the ordinate values.

dZ (x)dx

dZ (x)
dx

Zv5

Zt6

Zt5

Zt4

Zt3
Zt2

Zt1
Rz

Total height of the primary profile Pt
Total height of the roughness profile Rt
Total height of the waviness profile Wt
Sum of the height of the largest profile peak height Zp and the largest
profile valley depth Zv within the evaluation length

Sampling
lengthKurtosis of the primary profile Pku
Kurtosis of the roughness profile Rku
Kurtosis of the waviness profile Wku
Quotient of the mean quartic value of the ordinate values Z(x) and thefourth power of Pq, Rq, or Wq respectively, within a sampling length
1 1 Ir
Rku = Rq4 Ir∫Z4(x)dx0

Sampling lengthdZ (x)dx

dZ (x)
dx

The above equation defines Rsk. Psk and Wsk are defined in a similarmanner. Psk, Rsk, and Wsk are measures of the asymmetry of the probability density function of the ordinate values.

Sampling length

Maximum valley depth of the primary profile Pv
Maximum valley depth of the roughness profile Rv
Maximum valley depth of the waviness profile Wv
Largest profile valley depth Zv within a sampling length

1 1 Ir
Rsk = Rq3 Ir∫Z3(x)dx
0

Zv2

1 m
∑ Zt
m i=1 iHybrid Parameters
Root mean square slope of the primary profile PΔqRoot mean square slope of the roughness profile RΔqRoot mean square slope of the waviness profile WΔqRoot mean square value of the ordinate slope dZ/dX within a sampling length

Zp3

Pc, Rc, Wc =Rp

Amplitude Parameters (peak and valley)
Maximum peak height of the primary profile Pp
Maximum peak height of the roughness profile Rp
Maximum peak height of the waviness profile Wp
Largest profile peak height Zp within a sampling length

Rz

PG
52

Mean height of the primary profile elements Pc
Mean height of the roughness profile elements Rc
Mean height of the waviness profile elements Wc
Mean value of the profile element heights Zt within a sampling length

Skewness of the primary profile Psk
Skewness of the roughness profile Rsk
Skewness of the waviness profile Wsk
Quotient of the mean cube value of the ordinate values Z(x) and the
cube of Pq, Rq, or Wq respectively, within a sampling length

Zv3

Definition of Parameters
ISO 4287: 1997, Amd.1: 2009 (JIS B 0261: 2013)

RzJIS94

Sampling length

Peak count number based on the primary profile elements PPc
Peak count number based on the roughness profile elements RPc
Peak count number based on the waviness profile elements WPc
1
RPc = RSm

Used profile
Surface profile as measured
Roughness profile derived from the primary profile using aphase-correct high-pass filter

Arithmetic mean deviation of the profile Ra75
Arithmetic mean of the absolute values of the profile deviations fromthe mean line within the sampling length of the roughness profile(75%). This profile is obtained from a measurement profile using ananalog high-pass filter with an attenuation factor of 12db/octave and acutoff value ofλc.
1 ln
Ra75 = ∫|Z(x)|dx
ln 0

1 l 2
Z (x)dxl∫0with l as lp, lr, or lw according to the case.

Quick
QuickGuide
GuidetotoMeasurement
Measurement

PG

53

Surftest (Surface Roughness Testers)
Curves, Probability Density Function, and Related Parameters
Material ratio curve of the profile (Abbott-Firestone curve)
Curve representing the material ratio of the profile as a function of section level c
Mean Linec

PG
54

Sampling length

Probability density function(profile height amplitude distribution curve)
Sample probability density function of the ordinate Z(x) within theevaluation length
Mean Line

Evaluation lengthRmr(c),%

M l(c)
Pmr(c), Rmr(c), Wmr(c) = ln

Section height difference of the primary profile PδcSection height difference of the roughness profile RδcSection height difference of the waviness profile WδcVertical distance between two section levels of a given material ratioRδc = c (Rmr1) – c (Rmr2); Rmr1<Rmr2

Amplitude density

Table 1: Sampling lengths for aperiodic profile roughness
parameters (Ra, Rq, Rsk, Rku, R⊿q), material ratio curve,
probability density function, and related parametersRaµm(0.006)<Ra≤0.02
0.02<Ra≤0.1
0.1<Ra≤2
2<Ra≤10
10<Ra≤80Rδc

Rz, Rz1max.
µm(0.025)<Rz, Rz1max.≤0.1
0.1<Rz, Rz1max.≤0.5
0.5<Rz, Rz1max.≤10
10<Rz, Rz1max.≤50
50<Rz, Rz1max.≤200

C1

Sampling length lr
mm
0.08
0.25
0.8
2.5
8

Evaluation length ln
mm
0.4
1.25
4
12.5
40

Sampling length lr
mm
0.08
0.25
0.8
2.5
8

Evaluation length ln
mm
0.4
1.25
4
12.5
40

1) Rz is used for measurement of Rz, Rv, Rp, Rc, and Rt.
2) Rz1max. only used for measurement of Rz1max., Rv1max., Rp1max., and Rc1max..
0 10 20 30 40 50 60 70 80 90 100
Rmr0
Rmr

Relative material ratio of the primary profile Pmr
Relative material ratio of the roughness profile Rmr
Relative material ratio of the waviness profile Wmr
Material ratio determined at a profile section level Rδc, related to thereference section level c0

Pmr, Rmr, Wmr = Pmr (c1), Rmr (c1), Wmr (c1)where
c1 = c0 – Rδc (Pδc, Wδc)c0 = c (Pmr0, Rmr0, Wmr0)

PG

55

Table 3: Sampling lengths for measurement of periodic
roughness profile roughness parameters and periodic or aperiodic profile parameter Rsm
Rsm
mm0.013<Rsm≤0.04
0.04<Rsm≤0.13
0.13<Rsm≤0.4
0.4<Rsm≤1.3
1.3<Rsm≤4

Sampling length lr
mm
0.08
0.25
0.8
2.5
8

Estimate the sampling length from anestimated value and Tables 1 to 3

Measure Ra, Rz, Rz1max., or RSm according to
the estimated value of the sampling length

Roughness sampling length for
non-periodic profiles
ISO 4288: 1996 (JIS B 0633: 2001)

Table 2: Sampling lengths for aperiodic profile roughness
parameters (Rz, Rv, Rp, Rc, Rt)
C0

Fig.1 Procedure for determining the sampling length if it is not specified
Estimate Ra, Rz, Rz1max., or RSm according
to recorded waveforms, visual inspection, etc.

0 20 40 60 80 100

Material ratio of the primary profile Pmr (c)Material ratio of the roughness profile Rmr (c)Material ratio of the waviness profile Wmr (c)Ratio of the material length of the profile elements Ml (c) at a given
level c to the evaluation length

Procedure for determining a sampling length if it is not specified

Evaluation length ln
mm
0.4
1.25
4
12.5
40

Does each measured
value meet the parameter range of Table 1, 2, or 3 ?

NoChange to a longer
or shorter sampling length

Yes
Has a shorter sampling length been tried ?

No

Change to a shorter sampling length

Yes
Measure the parameter according
to the final sampling length

Fig.2 Procedure for determining the sampling length of a periodic profile if it is not specified.
Estimate RSm from a measured roughness profile

Estimate the sampling length froman estimated value and Table 3

Measure RSm according to the estimatedvalue of the sampling length

Does the measured value meet the condition of Table 3 ?

NoChange the sampling length so as tomeet the condition of Table 3

Yes
Measure the parameter according
to the final sampling length

Quick Guide to Measurement

Contracer (Contour Measuring Instruments)

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56

Traceable Angle

Circular-Arc / Linear Tracing

Contour analysis methods

Tolerancing with Design Data

The maximum angle at which a stylus can trace upwards or downwards
along the contour of a workpiece, in the stylus travel direction, isreferred to as the traceable angle. A one-sided sharp stylus with a tip
angle of 12° (as in the above figure) can trace a maximum 77° of up
slope and a maximum 87° of down slope. For a conical stylus (30°cone), the traceable angle is smaller. An up slope with an angle of 77°
or less overall may actually include an angle of more than 77° due tothe effect of surface roughness. Surface roughness also affects themeasuring force.
For model CV-3200/4500, the same type of stylus (SPH-71: one-sided
sharp stylus with a tip angle of 12°) can trace a maximum 77° of up
slope and a maximum 83° of down slope.

The locus traced by the stylus tip during vertical stylus movement canbe a circular arc or a straight line. Ensuring a straight-line locus entails
complex mechanics, while in the case of a circular-arc locus, if theamplitude of stylus displacement is large in the vertical direction, anerror (δ) in the recorded profile in the horizontal direction arises. (Seefigure at below)

You can analyze the contour with one of the following two methods
after completing the measurement operation.

Measured workpiece contour data can be compared with design data interms of actual and designed shapes rather than just analysis of individual
dimensions. In this technique each deviation of the measured contour
from the intended contour is displayed and recorded. Also, data fromone workpiece example can be processed so as to become the master
design data to which other workpieces are compared. This function isparticularly useful when the shape of a section greatly affects productperformance, or when its shape has an influence on the relationshipbetween mating or assembled parts.

Compensating for Arm Rotation

Data processing section and analysis program
The measured contour is input into the data processing section in realtime and a dedicated program performs the analysis using the mouse
and/or keyboard. The angle, radius, step, pitch and other data are directly
displayed as numerical values. Analysis combining coordinate systems canbe easily performed. The graph that goes through stylus radius correction
is output to the printer as the recorded profile.

When the stylus traces through a circular-arc, error arises in the X-axis
direction of the recorded profile. Possible methods for compensating forthis effect are as follows:

Best-fitting

1: Mechanical compensation
Down slopeδ

Data Combination

If there is a standard for surface profile data, tolerancing with design
data is performed according to the standard. If there is no standard, or if
tolerancing only with shape is desired, best-fitting between design data
and measurement data can be performed.
<Before best-fit processing>Up slope 77˚ or less 87˚ or less<After best-fit processing>

Conventionally, if tracing a complete contour is prevented by stylus
traceable-angle restrictions then it has to be divided into several sections
that are then measured and evaluated separately. This function avoids
this undesirable situation by combining the separate sections into one
contour by overlaying common elements (lines, points) onto each other.
With this function the complete contour can be displayed and various
analyses performed in the usual way.

Measured data

Measured data

Data 1Compensating for Stylus Tip Radius
A recorded profile represents the locus of the center of the ball tip rolling on a workpiece surface. (A typical radius is 0.025 mm.) Obviously
this is not the same as the true surface profile so, in order to obtain an
accurate profile record, it is necessary to compensate for the effect of
the tip radius through data processing.

r

2: Electrical compensationδStylusMeasuring arm
Fulcrum

Workpiece contour
Recorded profile
Stylus

δ: Unwanted displacement in X to be compensatedrr

Design data

Design data

Data 2

Data combination

The best-fit processing algorithm searches for deviations between bothsets of data and derives a coordinate system in which the sum of squaresof the deviations is a minimum when the measured data is overlaid on
the design data.

Measurement Examples

3: Software processing. To measure a workpiece contour that involves
a large displacement in the vertical direction with high accuracy, oneof these compensation methods needs to be implemented.

r: Stylus tip radius

If a profile is read from the recorder through a template or scale, it isnecessary to compensate for the stylus tip radius beforehand according
to the applied measurement magnification.

Accuracy
As the detector units of the X and Z axes incorporate scales, the magnification accuracy is displayed not as a percentage but as the linear
displacement accuracy for each axis.

Z axis Measurement Methods
Though the X axis measurement method commonly adopted is by meansof a digital scale, the Z axis measurement divides into analog methods(using a differential transformer, for example) and digital scale methods.
Analog methods vary in Z axis resolution depending on the measurement
magnification and measuring range. Digital scale methods have fixed
resolution.
Generally, a digital scale method provides higher accuracy than an
analog method.

Aspheric lens contour

Inner/outer ring contour of a bearing

Internal gear teeth

Female thread form

Male thread form

Gage contour

Overload Safety Cutout
If an excessive force (overload) is exerted on the stylus tip due, perhaps,
to the tip encountering a too-steep slope on a workpiece feature, ora burr, etc., a safety device automatically stops operation and sounds
an alarm buzzer. This type of instrument is commonly equipped withseparate safety devices for the tracing direction (X axis) load and verticaldirection (Z axis) load.

Quick Guide to Measurement

PG

57

Roundtest (Roundform Measuring Instruments)

PG
58

ISO 4291:1985 Methods for the assessement of departure from roundness -Measurement of variations in radius
ISO 1101:2012 Geometrical product specifications (GPS) -- Geometrical tolerancing -Tolerances of form, orientation, location and run-out
Roundness

Notation example

The line or surface must be contained within the tolerance zone formed between two planes a distance t apart and perpendicular to the datum
Notation example
A

Straightness

Any circumferential line must be contained within the tolerance zone
formed between two coplanar circles with a difference in radii of t

Perpendicularity

Any line on the surface must lie within the tolerance zone formed
between two parallel straight lines a distance t apart and in the direction specified

Notation example

ø0.08 A

59

A

Notation example

Notation example

øt

Notation example

0.1

PG

ø0.08 A

0.1

Datum A
Tolerance zone

Tolerance zone

Datum axistTolerance zone

Verification example using a roundness
measuring instrument

Verification example using a roundness
measuring instrumentt

Verification example using a roundness
measuring instrumentt

Tolerance zone

Verification example using a roundness
measuring instrument

Circular Runout (Radial and Axial)
The line must be contained within the tolerance zone formed between two coplanar and/or concentric circles a distance t apart concentric with or perpendicular to the datum

Flatness

Cylindricity

The surface must be contained within the tolerance zone formed
between two parallel planes a distance t apart

The surface must be contained within the tolerance zone formed
between two coaxial cylinders with a difference in radii of t

Notation example

Notation example

0.1

0.1

Specified direction: Radial direction Directionthat intersects the datum axial straight line
and is vertical to the datum axis line
0.1 A

Specified direction: Radial direction Directionthat intersects the datum axial straight line
and is vertical to the datum axis line
0.1 A

A

A

Notation example

Notation example
Tolerance zone

Tolerance zone

øtt

Verification example using a roundness
measuring instrumentt

Verification example using a roundness
measuring instrument

Datum axis

Datum axistTolerance zone

Verification example using a roundness
measuring instrument

Verification example using a roundness
measuring instrument
Tolerance zone

Total Runout (Radial and Axial)
Concentricity

Coaxiality

The center point must be contained within the tolerance zone formed
by a circle of diameter t concentric with the datum

The axis must be contained within the tolerance zone formed by a cylinder of diameter t concentric with the datum

Notation example

Notation example
A

A
Tolerance zone

The surface must be contained within the tolerance zone formed between two coaxial cylinders with a difference in radii of t, or planes a distance t
apart, concentric with or perpendicular to the datum
Specified direction: Radial direction Directionthat intersects the datum axial straight line
and is vertical to the datum axis line

Specified direction: Radial direction Directionthat intersects the datum axial straight line
and is vertical to the datum axis line

0.1 A

ø0.08 A

ø0.08 A

0.1 A

A

A

Notation example
Tolerance zoneøt

Notation example

øt

t

Datum
centerVerification example using a roundness
measuring instrument

Datum axis

Verification example using a roundness
measuring instrument

Datum axis
Tolerance zone

Verification example using a roundness
measuring instrument

Datum axistVerification example using a roundness
measuring instrument

Tolerance zone

Quick Guide to Measurement

Roundtest (Roundform Measuring Instruments)
Adjustment prior to Measurement

Centering
A displacement offset (eccentricity) between the Roundtest's turntableaxis and that of the workpiece results in distortion of the measured
form (limaçon error) and consequentially produces an error in thecalculated roundness value. The larger the eccentricity, the larger is theerror in calculated roundness.
Therefore the workpiece should be centered (axes made coincident)
before measurement. Some roundness testers support accurate measurement with a limaçon error correction function. The effectiveness of
this function can be seen in the graph below.

Effect of Filter Settings on the Measured Profile
Leveling
Any inclination of the axis of a workpiece with respect to the rotational
axis of the measuring instrument will cause an elliptic error. Levelingmust be performed so that these axes are sufficiently parallel.

Profiles can be filtered in various ways to reduce or eliminate unwanted detail, with a cut-off value set in terms of undulations per revolution (upr). The
effect of different upr settings is shown in the diagrams below, which illustrate how the measured roundness value decreases as lower upr settings
progressively smooth out the line.
Unfiltered

PG

Low-pass filter

ΔZq = 22.14 μm

ΔZq = 12.35 μm

ΔZq = 16.60 μm

15 upr

50 uprD

ΔZq = 18.76 μm

ø1mm
ø2mm
ø5mm
ø10mm
ø20mm
ø50mm
ø100mm
ø200mmΔZq = 14.50 μm

Error due to inclination (µm)

0.1010.000ø200mm
ø100mm
ø50mm

1.000

ø20mm
ø10mm
ø5mm

0.100

ø2mm
ø1mm

0.010
1

10

Eccentricity (µm)

15-500 upr

100

1000
0.001

Eccentricity versus roundness error0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Inclination (degrees)

Evaluating the Measured Profile Roundness ISO 12181-1: 2011* , ISO 4291: 1985*
5

Least Square Circle(LSC)

Minimum Zone Circles(MZC)

A circle is fitted to the measured profile such that the sum of the squaresof the departure of the profile data from this circle is a minimum. The
roundness figure is then defined as the difference between the
maximum deviation of the profile from this circle (highest peak to thelowest valley).

Two concentric circles are positioned to enclose the measured profilesuch that their radial difference is a minimum. The roundness figure isthen defined as the radial separation of these two circles.

1
Rmin

Rmax

Rmax

Evaluating the Measured Profile Roundness
Roundness testers use the measurement data to generate reference circles whose dimensions define the roundness value. There are four methods ofgenerating these circles, as shown below, and each method has individual characteristics so the method that best matches the function of the workpiece should be chosen. Each method results in a different center position for the reference circles and therefore affects the axial location of the circular feature measured.
Minimum Zone Circles(MZC)

Minimum Circumscribed Circle(MCC)

ΔZz = Rmax-Rmin
ΔZz: A symbol indicating roundness value by MZC.

Minimum Circumscribed
Circle (MCC)

Maximum inscribed
Circle (MIC)

The smallest circle that can enclose the measured profile is created. The
roundness figure is then defined as the maximum deviation of the
profile from this circle. This circle is sometimes referred to as the ‘ring
gage’ circle.

The largest circle that can be enclosed by the profile data is created.
The roundness figure is then defined as the maximum deviation of the
profile from this circle. This circle is sometimes referred to as the `plug
gage' circle.

Maximum inscribed Circle
(MIC)
Rmin

Rmax

Zq

Rmin

Rmax

Δ

Zz
Rmin
Rmax

Δ

Zc
Rmin
Rmax

Rmin

ΔZq = Rmax-Rmin
ΔZq: A symbol indicating roundness value by LSC.

Rmin
Δ

3

Roundness testers use the measurement data to generate reference circles whose dimensions define the roundness value. There are four
methods of generating these circles, as shown below, and each method has individual characteristics so the method that best matches
the function of the workpiece should be chosen.
Each method results in a different center position for the reference circles and therefore affects the axial location of the circular feature
measured.

Inclination versus elliptic error

Least Square Circle(LSC)

50-500 upr

100.000

1.00

0.01

150 upr500 upr2CR filter

Gaussian filter

Standard
Attenuation rate

ISO 4291: 1985*3
75 %ISO 12181-1: 2011*5
50 %Terms and abbreviated terms ISO 12181-1: 2011*15-150 upr

10.00

ΔZq = 22.04 μm

FilteringeEffect of eccentricity compensation function

100.00ΔZq = 20.72 μm

DDL

1000.0061θBand-pass filter
ΔZq = 17.61 μm

Roundness error (µm)

PG
60

ISO 4291:1985*3

Rmax

Δ

Zc
Rmin
Rmax

ΔZq = Rmax-Rmin
ΔZq : A symbol indicating roundness value by LSC.

ΔZz = Rmax-Rmin
ΔºZz : A symbol indicating roundness value by MZC

ΔZc = Rmax-Rmin
ΔºZc : A symbol indicating roundness value by MCC.

ΔZi = Rmax-Rmin
ΔZi : A symbol indicating roundness value by MIC.

A circle is fitted to the measured profile suchthat the sum of the squares of the departureof the profile data from this circle is a minimum. The roundness figure is then definedas the difference between the maximum
deviation of the profile from this circle (highest peak to the lowest valley).

Two concentric circles are positioned to
enclose the measured profile such that theirradial difference is a minimum. The roundness figure is then defined as the radial
separation of these two circles.

The smallest circle that can enclose the measured profile is created. The roundness figureis then defined as the maximum deviation of
the profile from this circle. This circle is sometimes referred to as the ‘ring gage’ circle.

The largest circle that can be enclosed by the
profile data is created. The roundness figureis then defined as the maximum deviation of
the profile from this circle. This circle is sometimes referred to as the `plug gage' circle.

ΔZc = Rmax-Rmin
ΔZc: A symbol indicating roundness value by MCC.

ΔZi = Rmax-Rmin
ΔZi: A symbol indicating roundness value by MIC.

FilteringStandard
Attenuation rate

2CR filter

Gaussian filter

ISO 4291: 1985*3
75 %ISO 12181-1: 2011*5
50 %Abbreviated terms
LSCI
LSCY
LSLI
LSPL
LCD
LFD
LRD
LSD
MICI
MICY
MCCI
MCCY
MZCI
MZCY
MZLI
MZPL
UPR

5

Terms
Least squares reference circle
Least squares reference cylinder
Least squares reference line
Least squares reference plane
Local cylindricity deviation
Local flatness deviation
Local roundness deviation
Local straightness deviation
Maximum inscribed reference circle
Maximum inscribed reference cylinder
Minimum circumscribed reference circle
Minimum circumscribed reference cylinder
Minimum zone reference circles
Minimum zone reference cylinder
Minimum zone reference lines
Minimum zone reference planes
Undulations per revolution

Parameters and abbreviated terms ISO 12181-1: 2011*

5

Reference element*
Minimum Least
Minimum Minimum
square circumscribed inscribedzone

Abbreviatedterms

Parameter

CYLtt
STRsg
STRIc
CYLp
FLTp
RONp
STRp
CYLt
FLTt
RONt
STRt
CYLv
FLTv
RONv
STRv
CYLq
FLTq
RONq
STRq
STRsa

Cylinder taper
Generatrix straightness deviation
Local generatrix straightness deviation
Peak-to-reference cylindricity deviation
Peak-to-reference flatness deviation
Peak-to-reference roundness deviation
Peak-to-reference straightness deviation
Peak-to-valley cylindricity deviation
Peak-to-valley flatness deviation
Peak-to-valley roundness deviation
Peak-to-valley straightness deviation
Reference-to-valley cylindricity deviation
Reference-to-valley flatness deviation
Reference-to-valley roundness deviation
Reference-to-valley straightness deviation
Root-mean-square cylindricity deviation
Root-mean-squareflatness deviation
Root-mean-square roundness deviation
Root-mean-square straightness deviation
Straightness deviation of the extracted median line

✓
✓
✓
✓
✓
✓
✓
✓
✓
✓

✓
✓

✓

✓

✓

✓

✓

✓

✓

✓
✓
✓
✓
✓
✓
✓
✓
✓

✓

✓
✓

* The reference elements to which the parameter can be applied.

Terms
abbreviatedterms
ISO 12181-1:**1 ISO/ DISand
1101: 1996
Geometrical ProductSpecifications(GPS) 2011
- Geometricaltolerancing - Tolerancing of form, orientation, location and run-out
5*2 ISO 5459 Technical drawings - Geometrical tolerancing - Datums and datum-systems for geometrical tolerances
Terms*3Abbreviated
ISO 4291: terms
1985 Methods for the assessmentof departure from roundness - Measurement of variations in radiussquares reference
circle*4 ISO LSCI
12181-2: 2011Least
Geometrical
Product Specifications(GPS) - Roundness - Part2: Specification operators
squares referencecylinder*5 ISO LSCY
12181-1: 2011Least
Geometrical
Product Specifications(GPS) - Roundness - Part 1: Vocabulary and parameters of roundness
LSLI
LSPL
LCD
LFD

Least squares reference line
Least squares reference plane
Local cylindricity deviation
Local flatness deviation

Quick Guide to Measurement

Hardness Testing Machines

F
F
F
2Fsinθ
HV=k =0.102 =0.102 2 2 =0.1891 2
S
S
d
d

F:N
d:mm

(3) Rockwell and Rockwell Superficial
To measure Rockwell or Rockwell Superficial hardness, first apply apreload force and then the test force to a specimen and return to thepreload force using a diamond indenter (tip cone angle: 120˚, tip radius:
0.2 mm) or a sphere indenter (steel ball or carbide ball). This hardness
value is obtained from the hardness formula expressed by the difference
in indentation depth h (µm) between the preload and test forces.
Rockwell uses a preload force of 98.07N, and Rockwell Superficial
29.42N. A specific symbol provided in combination with a type ofindenter, test force, and hardness formula is known as a scale. JapaneseIndustrial Standards (JIS) define various scales of related hardness.

The error in the calculated Vickers hardness is given by the following
formula. Here, Δd1, Δd2, and ‘a’ represent the measurement errorthat is due to the microscope, an error in reading an indentation, andthe length of an edge line generated by opposing faces of an indenter
tip, respectively. The unit of Δθ is degrees.
ΔHV
HV

ΔF

F

-2

Δd1

d

-2

Δd2

d

-

F:N
d:mm
c:ConstantF
F
FF
HK=k =0.102 =0.102 2 =1.451 2
A
A
cd
d

a2
3.5x10-3Δθd2

Relationship between Vickers Hardness and the Minimum Thickness of a Specimen
Hardness symbol

Minimum thicknessof specimen
t:mm
0.001
0.002
0.003
0.005

Vickers hardness
HV

d

2000

t
F
HV=0.1891 2
dt>1.5dh d/7
t: Thickness of specimen (mm)d: Diagonal length (mm)h: Depth of indentation (mm)

0.01

1000

0.02
0.03
0.05

500
300
200

0.1

100
50
30
20

[Example]
Specimen thickness t: 0.15 mm
Specimen hardness: 185HV1
Test force F: 9.807N (1 kgf)
Diagonal length d: 0.1 mm

0.2
0.3
0.5
1
2
3

Test force

HV0.0005

F:N
4.903x10-3

0.001

9.807x10-3

0.002
0.003
0.005

19.61x10-3
29.42x10-3
49.03x10-3

0.01

98.07x10-3

0.02
0.03
0.05

0.19610.29420.4903

0.02
0.03
0.05
0.1

0.1

0.9807

0.2
0.3
0.5

1.961
2.942
4.903

0.2
0.3
0.5

1

9.807

1

2
3
5

19.61
29.42
49.03

2

10

98.07

20
30
50

196.1
294.2
490.3

Diagonal lengthof indentation
d:mm
0.001
0.002
0.003
0.005
0.01

1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
10 20 30 40 50 60 70 80 90 100
HRD
HRC
HRA

Rockwell hardness

3.3
3.15
3
2.85
2.7
2.55
2.4
2.25
2.1
1.95
1.8
1.65
1.5
1.35
1.2
1.05
0.9
0.75
20 30 40 50 60 70 80 90 100
HRH
HRE
HRF
HRK
HRG
HRB

Minimum thickness of specimen (mm)As shown in the following formula, Knoop hardness is a value obtainedby dividing test force by the projected area A (mm2) of an indentation,
which is calculated from the longer diagonal length d (mm) of theindentation formed by pressing a rhomboidal diamond indenter(opposing edge angles of 172˚30' and 130˚) into a specimen with test
force F applied. Knoop hardness can also be measured by replacing
the Vickers indenter of a microhardness testing machine with a Knoop
indenter.

Minimum thickness of specimen (mm)(2) Knoop

Vickers hardness is a test method that has the widest application range,
allowing hardness inspection with an arbitrary test force. This test has
an extremely large number of application fields particularly for hardness
tests conducted with a test force less than 9.807N (1 kgf). As shownin the following formula, Vickers hardness is a value determined by
dividing test force F (N) by contact area S (mm2) between a specimen
and an indenter, which is calculated from diagonal length d (mm, meanof two directional lengths) of an indentation formed by the indenter(a square pyramidal diamond , opposing face angle θ =136˚) in thespecimen using a test force F (N). k is a constant (1/g =1/9.80665).

h

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(1) Vickers

Minimum thickness of specimen (mm)Relationship between Rockwell/Rockwell Superficial Hardness and the Minimum
Allowable Thickness of a Specimen

Methods of Hardness Measurement

1.4
1.2

HRT

1.0

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0.8
0.6
HRN

0.4

0.2
0.0
10 20 30 40 50 60 70 80 90 100
15N
30N
15T
45N
30T
45T

Rockwell hardness

Rockwell hardness

Rockwell Hardness Scales
Scale
A
D
C
F
B
G
H
E
K
L
M
P
R
S
V

IndenterDiamondBall with adiameter of
1.5875 mm
Ball with adiameter of
3.175 mmBall with adiameter of
6.35 mmBall with adiameter of
12.7 mm

Test force (N)
588.4
980.7
1471
588.4
980.7
1471
588.4
980.7
1471
588.4
980.7
1471
588.4
980.7
1471

Rockwell Superficial Hardness Scales
Application
Carbide, sheet steel
Case-hardened steel
Steel (100 HRB or more to 70 HRC or less)
Bearing metal, annealed copper brass
Hard aluminum alloy, beryllium copper,
phosphor bronze
Bearing metal, grinding wheel
Bearing metal
Bearing metal
Plastic, lead
plastic

Scale
15N
30N
45N
15T
30T
45T
15W
30W
45W
15X
30X
45X
15Y
30Y
45Y

IndenterDiamondBall with adiameter of
1.5875 mm
Ball with adiameter of
3.175 mmBall with adiameter of
6.35 mmBall with adiameter of
12.7 mm

Test force (N)
147.1
294.2
441.3
147.1
294.2
441.3
147.1
294.2
441.3
147.1
294.2
441.3
147.1
294.2
441.3

Application
Thin surface-hardened layer on steel
such as carburized or nitrided
Sheet of mild steel, brass, bronze, etc.
Plastic, zinc, bearing alloy
Plastic, zinc, bearing alloy
Plastic, zinc, bearing alloy

Quick Guide to Measurement

Coordinate Measuring Machines
Performance Assessment Method of Coordinate Measuring Machines

Moving-Bridge Type CMM

Regarding the performance assessment method of CMM, a revision of ISO
10360 series was issued in 2003, and was partially revised in 2009.
The following describes the standard inspection method including the revised
content.

This type is configured with the vertically moving ram (Z axis)
mounted on a carriage, the carriage (X axis) horizontally
moving on a bridge structure that is supported by the baseand guided horizontally to form the Y axis. A workpiece isloaded on the base.
Many Mitutoyo CMM models have adopted this type ofstructure, achieving high accuracy, high speed and highacceleration. Mitutoyo offers a strong lineup of CMMs ofthis type from compact models through to the largest sizes
found in the inspection room.

X

Z

1
2
3
4
5
6

Item
Terms
Length measurement
Rotary table equipped CMM
Scanning measurement
Single/Multi-styli measurement
Software inspection

Year of issue
2000
2009
2000
2000
2010
2001

Maximum permissible length measurement error E0,MPE [ISO 10360-2:2009]
Using the standard CMM with specified probe, measure 5 different calibrated lengths 3 times each in 7 directions within the measuring volume (as indicated in Figure1), making a total of 105 measurements.
If these measurement results, including the allowance for the uncertainty of measurement, are equal to or less than the values specified by the manufacturer, then it
proves that the performance of the CMM meets its specification.
The result of OK/NG is required to be judged considering the uncertainties.
The maximum permissible error (standard value) of the test may be expressed in any of the following three forms (unit: µm).
Length meas. error 3（Z）

This type is configured with the vertically moving ram (Zaxis) mounted on a carriage, the carriage (X axis) moving
horizontally on a bridge structure fixed to the base and atable (Y axis) moving horizontally on the base. A workpieceis loaded on the moving table.
Mitutoyo's Ultrahigh-accuracy CNC CMM LEGEX Series has
adopted this structure type, providing the world's highest
accuracy by minimizing error sources through exhaustive
investigation and analysis.

Length meas. error 5

Length meas. error 4

Length meas. error 6
Z
Y

Length meas. error 7

Length meas. error 2（Y）

X

Z

Z

Y
X

Length meas. error 1（X）

Y
X

Figure 1 Measuring directions to obtain length measurement error⎧⎨⎩

E 0,MPE（MPEE）＝ A ＋ L/K ≤ B
E 0,MPE（MPEE）＝ A ＋ L/K
E 0,MPE（MPEE）＝ B

A: Constant (µm) specified by the manufacturer
K: Dimensionless constant specified by the manufacturer
L: Measured length (mm)
B: Upper limit value (µm) specified by the manufacturer

Note: ISO 10360-2:2009 requires measurement in 4 different directions and recommends measurement parallel to each axis, while ISO 10360-2:2001 specified
the measurement "in arbitrary 7 directions."

The following error definitions were added in ISO 10360-2:2009.

Maximum Permissible Length Measurement Error / Length Measurement Error whenZ-axis stylus offset is 150 mm E150, MPE [ISO 10360-2:2009]

Horizontal-Arm Type CMM

In addition to length measurement in 7 directions, ISO 10360-2:2009 specifies
measuring in 2 lines over the diagonal YZ or XZ plane with probe offset.
Note: The stylus offset is set at 150 mm as default.

Y
Z

X

Figure 2 Length measurement error when Z-axis stylus offset is 150mm

Maximum Permissible Limit of the Repeatability Range of Length Measurement R0, MPL [ISO 10360-2:2009]
6.0

Calculate the maximum value from the results of three repeated measurements.

4.0

Bridge / Floor Type CMM
This type is configured with the vertically moving ram (Zaxis) mounted on a carriage, the carriage (X axis) moving
horizontally on a double bridge structure (Y axis) that is
supported on a hard floor. A workpiece is set down directlyon the floor.
Mitutoyo's Ultralarge Separate Guide CNC CMM has
adopted this type that incorporates Mitutoyo's original
structure (moving bridge on-floor installation type). It
allows high-accuracy measurement of a large, heavy
workpiece, featuring the world's largest measuring range.

ISO Standard No.
ISO 10360-1
ISO 10360-2
ISO 10360-3
ISO 10360-4
ISO 10360-5
ISO 10360-6

Y

Fixed-Bridge Type CMM

This type is configured with the horizontally movingram (Z axis) mounted on a carriage, the carriage (Y axis)
vertically moving on a column supported by the base andthe column (X axis) moving horizontally on the base. A
workpiece is loaded on the base.
Mitutoyo In-line Type CNC CMM MACH-3A Series
has adopted this structure type, attaining high-speed
positioning, space-saving and durability to be compatible
with line-side / in-line installation.

Table 1 ISO 10360 series

Error［µm］

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Mitutoyo coordinate measuring machines use four structure types that provide the benefits of excellent stability, high accuracy, high measuring speed,
convenience of workpiece clamping, etc.

2.0

R0

0.0

-2.0

Z

-4.0

Y

-6.0

X

1
0

2
200

3

Standard value

400

600

Measurement length [mm]800

Figure 3 Repeating range of length measurement

Maximum Permissible Radial Four-Axis Error MPE FR,
Maximum Permissible Tangential Four-Axis Error MPE FT, andMaximum Permissible Axial Four-Axis Error MPE FA [ISO 10360-3:2000]
The test procedure under this standard is to place two standard spheres on the rotary table as shown in Figure 4.
Rotate the rotary table to a total of 15 positions including 0˚, 7 positions in the plus (+) direction, and 7 positions in theminus (-) direction and measure the center coordinates of the two spheres in each position. Then, add the uncertaintyof the standard sphere shape to each variation (range) of radial direction elements, connecting direction elements, androtational axis direction elements of the two standard sphere center coordinates. If these calculated values are less than
the specified values, the evaluation test is passed.

Z
Sphere B
Y

hB
r

X
h

Sphere A

hA

Figure 4 Evaluation of a CMM with a rotary table

Quick Guide to Measurement

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Coordinate Measuring Machines

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Maximum Permissible Scanning Probing Error MPE THP [ISO 10360-4:2000]

Measurement Uncertainty of CMM

This is the accuracy standard for a CMM if equipped with a scanning probe. The test procedure under this standard is to perform a scanning measurement in 4 planeson the standard sphere and then, for the least squares sphere center calculated using all the measurement points, calculate the radial range (dimension ‘A’ in Figure5) within which all measurement points exist. Based on the least squares sphere center calculated above, calculate the radial distance between the calibrated standard
sphere radius and the maximum measurement point and the minimum measurement point, and take the larger distance (dimension ’B’ in Figure 5). Add an extended
uncertainty that combines the uncertainty of the stylus tip shape and the uncertainty of the standard test sphere shape to each A and B dimension. If both calculated
values are less than the specified values, this scanning probe test is passed.

Measurement uncertainty is an indication used for evaluating reliability of measurement results.
In ISO 14253-1:1998, it is proposed to consider the uncertainty when evaluating the measurement result in reference to the specification.
However, it is not easy to estimate the uncertainty of the measurement performed by a CMM.
To estimate the uncertainty of the measurement, it is necessary to quantify each source of uncertainty, and determine how it propagates to the measurement
result. The CMM is subject to all types of settings that determine how the measurement should be performed, such as measurement point distribution, or datum
definition, according to the drawing instruction or operator's intention. This feature makes it harder to detect the source of uncertainty influencing the result.
Taking circle measurement as an example, just a difference of one measurement point and its distribution causes the necessity of recalculation of the uncertainty.
Also, there are many sources of uncertainty to be considered with the CMM and their interactions are complex.
Because of the above, it is almost impossible to generalize on how to estimate measurement uncertainty of the CMM.

StylusLeast square
sphere45ºCalibrated value ofstandard sphere radius

Measurement task

Scan plane 2

Data processing

Positioning of measuring
pointsScan plane 1
Scan plane 3

Least square spherecenter

CMM

Environment

Uncertainty of center
position
Uncertainty of circle profile

Probe

Workpiece

A

Scan plane 4

Uncertainty of measurement
Measurement point

B

Figure 5 Target measurement planes for the maximum permissible scanning probing error and its evaluation concept

Maximum Permissible Single Stylus Form ErrorPFTU, MPE [ISO 10360-5:2010]
This measurement was included in the dimensional measurement in ISO 10360-2:2001. However, it is specified as "CMMs using single and multiple stylus contacting probing systems" in ISO 10360-5:2010.
The measurement procedure has not been changed, and the following should be performed.
Measure the defined target points on a standard sphere (25 points, as in Figure 6) and use all the results to calculate the center position of the sphere by a leastsquares method.
Then, calculate the distance R from the center position of the sphere by a least squares method for each of the 25 measurement points, and obtain the radius difference Rmax - Rmin. If the radius difference, to which a compound uncertainty of forms of the stylus tip and the standard test sphere are added, is equal to orless than the specified value, it can be judged that the probe has passed the test.

22.5゜
22.5゜
a
22.5゜

Example of circle measurement by CMM

Major contributions that cause uncertainty in CMM measurement results

Measurement uncertainty of the CMM and the Virtual CMM software
The Virtual CMM software* enables straightforward, automated estimation of the measurement uncertainty of a CMM. The software simulates a CMM on a PC
based on its machine characteristics and performs virtual (simulated) measurements. The simulated measurements are performed according to the part program created by the machine operator. The machine's performance is evaluated from experimental values based on geometrical characteristics of the actual machine, probing
characteristics, and temperature environment, etc., and the measurement uncertainty of the CMM is estimated by the software package.
ISO15530 Part 4 (ISO / TS 15530-4 (2008)) defines how to verify the validity of task-specific measurement uncertainty using computer simulations.
Virtual CMM conforms to this specification.
CMM

Probe

Environment

Quantification of CMM uncertainty elements by experiment

22.5゜

Note: Virtual CMM is a software package originally developed by PTB (Physikalisch-Technische Bundesanstalt).
Relevant parts of ISO15530: Geometrical Product Specifications (GPS) -- Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement -22.5゜Part 3: Use of calibrated workpieces or measurement standards
Part 4: Evaluating task-specific measurement uncertainty using simulation [Technical Specification]

Figure 6 T arget points for determining the Maximum Permissible Probing Error

Quick Guide to Measurement

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Quick Guide to Precision Measuring Instruments
No. E11003(6)Issued in December, 2021
Issued by Mitutoyo Corporation
20-1, Sakado-1Chome, Takatsu-ku, Kawasaki-shi,
Kanagawa 213-8533, Japan

Our products are classified as regulated items under Japanese Foreign Exchange and Foreign
Trade Law. Please consult us in advance if you wish to export our products to any othercountry.
If the purchased product is exported, even though it is not a regulated item (Catch-All controls item), the customer service available for that product may be affected. If you have any
questions, please consult your local Mitutoyo sales office.

Mitutoyo reserves the right to change any or all aspects of any product specification, including prices, designs and service content, without notice.

Catalog No. E11003(6)Mitutoyo Corporation
20-1, Sakado 1-Chome, Takatsu-ku, Kawasaki-shi,
Kanagawa 213-8533, Japan

Quick Guide to Precision Measuring Instruments

https://www.mitutoyo.co.jp

580 2112(6)g-(CH)NE-(JP11), Printed in Japan